Normal & Z distribution The Height distribution of 700 Scottish men is modelled by the normal distribution, with mean 174 cm and standard deviation 10 cm. a) Calculate the probability of a man being greater than 180 cm in height b) Estimate the number of men with height greater than 180 cm (to 3 s.f.) c) If 5% of the Scottish men have been selected to join a basketball team by having a height of x or more, estimate the value of x (to 3 s.f.) marks) (4 d) Calculate the probability of a man being less than 150 cm in height e) Estimate the number of men with height of less than 150 cm (to 1 s.f.) f) Calculate the probability of a man being between 170 and 190 cm in height

Answers

Answer 1

The estimated number of men with a height of less than 150 cm is approximately .

To solve these problems, we'll use the properties of the normal distribution and the standard normal distribution (Z-distribution). The Z-distribution is a standard normal distribution with a mean of 0 and a standard deviation of :

1. We can convert values from a normal distribution to the corresponding Z-scores and use the Z-table or a calculator to find probabilities.

a) Calculate the probability of a man being greater than 180 cm in height:

First, we need to calculate the Z-score for a height of 180 cm using the formula:

Z = (X - μ) / σ

where X is the value (180 cm), μ is the mean (174 cm), and σ is the standard deviation (10 cm).

Z = (180 - 174) / 10 = 6 / 10 = 0.6

Using the Z-table or a calculator, we can find the probability of Z > 0.6, which is approximately 0.2743. Therefore, the probability of a man being greater than 180 cm in height is approximately 0.2743.

b) Estimate the number of men with height greater than 180 cm:

To estimate the number of men, we can use the probability from part (a) and multiply it by the total number of men (700):

Number of men = Probability of being greater than 180 cm * Total number of men

Number of men = 0.2743 * 700 = 191.01 (rounded to 3 significant figures)

Therefore, the estimated number of men with a height greater than 180 cm is approximately 191.

c) If 5% of the Scottish men have been selected to join a basketball team by having a height of x or more, estimate the value of x:

We need to find the Z-score that corresponds to the probability of 0.95 (1 - 0.05), as it represents the percentage below the cutoff height.

Using the Z-table or a calculator, we find that the Z-score corresponding to a probability of 0.95 is approximately 1.645.

Now, we can calculate the height corresponding to this Z-score using the formula:

Z = (X - μ) / σ

Rearranging the formula to solve for X:

X = Z * σ + μ

X = 1.645 * 10 + 174

X = 16.45 + 174

X ≈ 190.45

Therefore, the estimated value of x (cutoff height for joining the basketball team) is approximately 190.45 cm.

d) Calculate the probability of a man being less than 150 cm in height:

First, we calculate the Z-score for a height of 150 cm:

Z = (X - μ) / σ

Z = (150 - 174) / 10

Z = -24 / 10

Z = -2.4

Using the Z-table or a calculator, we can find the probability of Z < -2.4, which is approximately 0.0082. Therefore, the probability of a man being less than 150 cm in height is approximately 0.0082.

e) Estimate the number of men with a height of less than 150 cm:

To estimate the number of men, we can use the probability from part (d) and multiply it by the total number of men (700):

Number of men = Probability of being less than 150 cm * Total number of men

Number of men = 0.0082 * 700 = 5.74 (rounded to 1 significant figure)

Therefore, the estimated number of men with a height of less than 150 cm is approximately.

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Related Questions

The probability that truck A will drop in price is 0.69 while the probability that truck B will drop in price is 0.8. The probability of either or both trucks droppingng in price is 0.99. A= truck A will drop in price B= truck B will drop in price Report numeric answers to at least 2 decimal places. convert to percent. 1. Draw a completed Venn diagram and upload it here 1. What is the probability that a) truck B will not drop in price? P( Bˉ ) b) only truck A will drop in price? P(A∩ Bˉ ) c) both trucks will drop in price? P(A∩B) d) both trucks will not drop in price? P( Aˉ ∩ Bˉ ) e) only one truck will drop in price (not both)? f) no more than one truck will drop in price? P( Aˉ ∪ Bˉ ) g) truck B will drop in price given that truck A dropped in price? P(B∣A)

Answers

1)  The Venn diagram shows the probability of each event of Truck A and Truck B. It also shows the probability of either or both trucks dropping in price.

2) Probability

a) P(Bˉ) = 0.20 or 20%

b) P(A∩ Bˉ) = 0.49 or 49%

c) P(A∩B) = 0.50 or 50%

d) P(Aˉ ∩ Bˉ) = 0.01 or 1%

e) P(A∪B) − P(A∩B) = 0.69 + 0.80 - (0.50) = 0.99 - 0.50 = 0.49 or 49%

f) P(Aˉ ∪ Bˉ) = 0.21 or 21%

g) P(B|A) = P(A∩B) / P(A)

= 0.50 / 0.69 ≈ 0.72 or 72%

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A manufacturer of contact lenses is studying the curvature of the lenses it sells. In particular, the last 500 lenses sold had an average curvature of 0.5. The population is a. the 500 lenses. b. 0.5. c. the lenses sold today. d. all the lenses sold by the manufacturer. e. none of the above

Answers

The standard deviation of times taken for germination for cauliflower seeds is approximately 0.70 days.

To find the standard deviation of times taken for germination for cauliflower seeds, we can use the concept of the standard normal distribution.

Let's denote the standard deviation as σ.

Given that 90% of the cauliflower seeds germinate in 6.2 days or more, we can find the z-score corresponding to this percentile.

The z-score can be calculated using the formula:

z = (x - μ) / σ

where:

x = 6.2 (the value of interest)

μ = 7.1 (mean)

σ = standard deviation (to be determined)

To find the z-score, we can rearrange the formula as follows:

σ = (x - μ) / z

Substituting the given values:

σ = (6.2 - 7.1) / z

To find the z-score corresponding to the 90th percentile, we look up the value in the standard normal distribution table or use a calculator. The z-score for a cumulative probability of 0.9 is approximately 1.2816.

Substituting the z-score into the formula:

σ = (6.2 - 7.1) / 1.2816

Performing the calculation:

σ = -0.9 / 1.2816 ≈ -0.7020

Rounding the standard deviation to two decimal places, we get:

σ ≈ -0.70

Therefore, the standard deviation of times taken for germination for cauliflower seeds is approximately 0.70 days.

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The manufacturer of contact lenses is studying the curvature of the lenses it sells. In particular, the last 500 lenses sold had an average curvature of 0.5. In the context of statistical analysis, the population refers to all of the individuals, objects, measurements, or data points that have a common characteristic of interest to the researcher.

The population is usually denoted by "N." In this case, the population refers to all the lenses sold by the manufacturer.A sample is a subset of the population, and it is typically denoted by "n." A sample is used to draw inferences about the population. In this case, the sample is the last 500 lenses sold by the manufacturer. Therefore, the correct answer is (d) all the lenses sold by the manufacturer. The population in this context includes all the lenses sold by the manufacturer, not just the last 500 lenses. It is essential to understand the difference between population and sample, as it has important implications for statistical inference, generalizability of results, and accuracy of conclusions.

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f(x)=x³−2x a) Find the average rate of change when x=4 and h=0.5 b) Find the average rate of change between x=4 and x=4.01 (You only need to do part a and b for #17 only.)

Answers

a) The average rate of change when x = 4 and h = 0.5 is -87.25.

b) The average rate of change between x = 4 and x = 4.01 is 1612.0301.

a) To find the average rate of change when x = 4 and h = 0.5 for the function f(x) = x³ - 2x, we can use the formula:

The average rate of change = (f(x + h) - f(x)) / h

Substituting the given values:

Average rate of change = (f(4 + 0.5) - f(4)) / 0.5

To calculate f(4 + 0.5) and f(4):

f(4 + 0.5) = (4 + 0.5)³ - 2(4 + 0.5) = 4.375

f(4) = 4³ - 2(4) = 48

Substituting these values into the formula:

The average rate of change = (4.375 - 48) / 0.5

The average rate of change = (-43.625) / 0.5

The average rate of change = -87.25

Therefore, the average rate of change when x = 4 and h = 0.5 for the function f(x) = x³ - 2x is -87.25.

b) To find the average rate of change between x = 4 and x = 4.01 for the function f(x) = x³ - 2x, we can use the same formula:

The average rate of change = (f(x₂) - f(x₁)) / (x₂ - x₁)

Substituting the given values:

The average rate of change = (f(4.01) - f(4)) / (4.01 - 4)

To calculate f(4.01) and f(4):

f(4.01) = (4.01)³ - 2(4.01) = 64.120301

f(4) = 4³ - 2(4) = 48

Substituting these values into the formula:

The average rate of change = (64.120301 - 48) / (4.01 - 4)

The average rate of change = 16.120301 / 0.01

The average rate of change = 1612.0301

Therefore, the average rate of change between x = 4 and x = 4.01 for the function f(x) = x³ - 2x is 1612.0301.

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It has been found from experience that an average of three customers use the drive-through facility at a local fast-food outlet in any given 10 minute period.
What is the probability that more than two customers will use the drive-through facility in any randomly selected five minute period?

Answers

The probability of more than two customers using the drive-through facility in any randomly selected five minute period can be calculated using the Poisson distribution.

The Poisson distribution is commonly used to model the number of events occurring in a fixed interval of time, given the average rate of occurrence. In this case, the average rate is three customers in a 10 minute period.

To calculate the probability of more than two customers using the drive-through facility in a five minute period, we can first calculate the average rate of occurrence in a five minute period. Since the average rate is three customers in 10 minutes, the average rate in five minutes would be (3/10) * 5 = 1.5 customers.

Next, we can use the Poisson distribution formula to calculate the probability. The formula is P(X > k) = 1 - P(X ≤ k), where X is the random variable representing the number of customers and k is the desired number of customers (in this case, k = 2).

Using the Poisson distribution with an average rate of 1.5, we can calculate P(X > 2) = 1 - P(X ≤ 2). This probability can be obtained using either a Poisson distribution table or a calculator.

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What is the value of the Pearson coefficient of skewness for a distribution with a mean of 14, median of 13 and variance of 7?
What is the value of the Pearson coefficient of skewness for a distribution with a mean of 14, median of 13 and variance of 7?

Answers

The distribution value's skewness Pearson coefficient will be 21.

Given that the median is 13 and the variance of 7, the mean value is 14.

We can see the difference between the mean and median is multiplied by three to determine Pearson's coefficient of skewness. Based on dividing the outcome by the standard deviation, And the random variable, sample, statistical population, data set, or probability distribution's standard deviation is equal to the square root of its variance.

To find Pearson's coefficient of skewness, use the following formula:

Skewness=(3(Mean-Median))÷standard deviation

Replace the values ,

Skewness=(3(14-13 ))÷1/7

Skewness=(3×1)÷1/7

Skewness=3×7

Skewness=21

Therefore, for a distribution with a mean of 14, a median of 13 , and a variance of 7, the value of the Pearson coefficient of skewness is 21.

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In the following, convert an area from one normal distribution to an equivalent area for a different normal distribution. Show details of your calculation. Draw sketches of both normal distributions, find and label the endpoints, and shade the regions on both curves.
The area to the right of 50 in a N(40, 8) distribution converted to a standard normal distribution.

Answers

The area to the right of 50 in an N(40, 8) distribution converted to a standard normal distribution is 0.1056.

Given data: μ = 40, σ = 8 and X = 50.To find: The area to the right of 50 in an N(40, 8) distribution converted to a standard normal distribution.

For a normal distribution N(μ, σ), the z-score is given by:z = (X - μ) / σPutting the given values in the above formula, we get:z = (50 - 40) / 8 = 1.25The equivalent area in the standard normal distribution can be found using the standard normal table as:

Area to the right of 1.25 in the standard normal distribution = 1 - Area to the left of 1.25 in the standard normal distribution.

Let us draw the two normal distributions to better understand the conversion: Normal Distribution N(40, 8)

Normal Distribution N(0, 1)

We need to find the area to the right of X = 50 in the N(40, 8) distribution. The shaded region is shown below:

Shaded region in N(40, 8) distributionNow, we need to find the equivalent area in N(0, 1) distribution.

For this, we need to find the area to the right of z = 1.25 in N(0, 1) distribution. The shaded region is shown below:

The shaded region in N(0, 1) distribution

So, the area to the right of 50 in an N(40, 8) distribution converted to a standard normal distribution is 0.1056 (approx).

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X~ N(120, 4²) You N / 115,3²) P(x > Y) = ?

Answers

For the given expression,

P(X > Y) = 1 - P(Y > X)

Here we have to standardize the random variables X and Y,

which means we convert them into standard normal variables Z.

We can do that by subtracting the mean and dividing by the standard deviation,

⇒ Z_X = (X - μ_X) / σ_X

           = (X - 120) / 4 Z_Y

           = (Y - μ_Y) / σ_Y

           = (Y - 115.3) / √(3²)

           = (Y - 115.3) / 3

Next, we need to find the probability that Z_X is greater than Z_Y.

We can do that by using the standard normal distribution table, or by using a calculator that has the standard normal distribution function built-in.

⇒ P(Z_X > Z_Y) = P((X - 120) / 4 > (Y - 115.3) / 3)

                          = P(X - 120 > (Y - 115.3)4/3)

                          = P(X > (Y - 115.3) 4/3 + 120)

Now, we need to find the value of (Y - 115.3)4/3 + 120 that corresponds to a standard normal variable Z with a certain probability.

Use a standard normal distribution table to find this value,

For example,

If we want to find P(Z > 1.96),

which corresponds to a probability of 0.025,

we can look up the value of 1.96 in the standard normal distribution table and find that it corresponds to an area of 0.025 to the right of the mean.

So, we can find P(Z_X > Z_Y) by finding the appropriate value in the standard normal distribution table and subtracting it from 1 (since we want the probability of X being greater than Y)

⇒ P(Z_X > Z_Y)  = 1 - P(Z_X ≤ Z_Y)

                           = 1 - P(Z_Y ≥ Z_X)

                           = 1 - P(Z_Y > Z_X)

Hence,  P(X > Y) = 1 - P(Y > X)

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The College Board claims that less than 50% of college freshmen have declared a major. In a survey of 300 randomly selected college freshmen, they found that 126 have declared a major. Test the College Board’s claim at a 1% significance level.
Calculate the test statistic. ANS: z = -2.77
Find the p-value. ANS: p-value = 0.0028
I HAVE PROVIDED THE ANS PLEASE SHOW HOW TO SOLVE IT

Answers

Using the sample size and sample proportion;

a. The test statistic is Z = -2.77

b. The p-value is approximately 0.0028.

What is the test statistic?

To test the College Board's claim, we can use a one-sample proportion test. Let's calculate the test statistic and the p-value step by step.

Given:

Sample size (n) = 300Number of successes (126) = number of freshmen who declared a major

Step 1: Set up the hypotheses:

H₀: p ≥ 0.50 (Claim made by the College Board)

H₁: p < 0.50 (Alternative hypothesis)

Step 2: Calculate the sample proportion (p):

p = 126/300

p = 0.42

Step 3: Calculate the test statistic (Z-score):

The formula for the Z-score in this case is:

Z = (p - p₀) / √(p₀ * (1 - p₀) / n)

Where p₀ is the hypothesized proportion under the null hypothesis (0.50 in this case).

Z = (0.42 - 0.50) / √(0.50 * (1 - 0.50) / 300)

  = -0.08 / √(0.25 / 300)

  = -0.08 / √0.00083333

  ≈ -2.77

The test statistic is approximately -2.77.

Step 4: Find the p-value:

To find the p-value, we need to calculate the area under the normal distribution curve to the left of the test statistic (-2.77) using a Z-table or statistical software.

From the Z-table or software, we find that the p-value corresponding to a Z-score of -2.77 is approximately 0.0028.

The p-value is approximately 0.0028.

Based on the p-value being less than the significance level (1%), we reject the null hypothesis and conclude that there is evidence to suggest that the proportion of college freshmen who have declared a major is less than 50%, as claimed by the College Board.

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4. Suppose the random variable X comes with the density function of 2x/0² for some parameter 0, when x = [0, a(0)], where a(0) is some function of 0. Otherwise, the density equals zero. Based on a sample of size n answer the following. (a) Show that a(0) = 0. (b) What is CDF of X? (c) What is the MLE for ? (d) Denote the above MLE by T. Show that the distribution of T/0 is free of 0.

Answers

a. the interval is [0, a(0)], this means that a(0) must be equal to 0. b. the CDF of X is

F(x) = x²/θ for x in the interval [0, a(0)]

F(x) = 0 for x outside the interval [0, a(0)]

c. the maximum likelihood estimator (MLE) for θ is θ = 0. d. the distribution of T/θ is free of θ because it is the same as the distribution of T, which does not depend on θ.

(a) To determine the value of a(0), we need to find the upper limit of integration for the density function. We know that the density function is zero outside the interval [0, a(0)]. For the density function to be valid, the integral over the entire range of X must equal 1.

Integrating the density function over the interval [0, a(0)]:

∫(2x/θ) dx = [x²/θ] evaluated from 0 to a(0) = a(0)²/θ

To satisfy the condition that the integral equals 1, we have:

a(0)²/θ = 1

a(0)² = θ

a(0) = √θ

Since we are given that the interval is [0, a(0)], this means that a(0) must be equal to 0.

(b) The cumulative distribution function (CDF) is obtained by integrating the density function. In this case, the density function is 2x/θ for x in the interval [0, a(0)], and zero otherwise.

To find the CDF, we integrate the density function:

∫(2x/θ) dx = [x²/θ] evaluated from 0 to x = x²/θ - 0 = x²/θ

Therefore, the CDF of X is:

F(x) = x²/θ for x in the interval [0, a(0)]

F(x) = 0 for x outside the interval [0, a(0)]

(c) To find the maximum likelihood estimator (MLE) for θ, we use the likelihood function based on a sample of size n. Since the density function is defined only for x in the interval [0, a(0)], the likelihood function is the product of the density function evaluated at the observed values.

For a sample of n observations, x₁, x₂, ..., xₙ, the likelihood function L(θ) is:

L(θ) = (2x₁/θ) * (2x₂/θ) * ... * (2xₙ/θ) = (2ⁿ * x₁ * x₂ * ... * xₙ) / θⁿ

To find the MLE for θ, we maximize the likelihood function with respect to θ. Taking the logarithm of the likelihood function and differentiating with respect to θ:

ln(L(θ)) = ln(2ⁿ * x₁ * x₂ * ... * xₙ) - n ln(θ)

Setting the derivative equal to zero:

d(ln(L(θ)))/dθ = 0

-n/θ + 0 = 0

θ = 0

Therefore, the maximum likelihood estimator (MLE) for θ is θ = 0.

(d) Denoting the MLE by T, we want to show that the distribution of T/θ is free of θ.

To do this, we need to find the distribution of T/θ, which is the ratio of two random variables. Since θ is known to be 0, we can consider T/θ as the ratio of T and a constant, which is equivalent to T.

Therefore, the distribution of T/θ is the same as the distribution of T, which is independent of θ.

In conclusion, the distribution of T/θ is free of θ because it is the same as the distribution of T, which does not depend on θ.

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A satellite flies
93288
93288 miles in
11.96
11.96 hours. How many miles has it flown in
8.9
8.9 hours?

Answers

The satellite will fly a distance of 69420 miles in 8.9hours

What is velocity?

Velocity is the rate at which a body moves. It can also be defined as the rate of change of distance with time. It can also be measured in m/s or other derived units. it is a vector quantity.

Velocity is expressed as;

V = distance of time

the velocity of the satellite

= 93288/11.96

= 7800 miles per hour

In 8.9 hours , the distance he will cover is calculated as

d = 8.9 × 7800

d = 69420 miles

Therefore the satellite will cover a distance of 69420 miles in 8.9hours

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1) True or False: Consider a value of r = 0.500. It would be
appropriate to multiply this value by 100 and intepret it as
representing 50%.

Answers

Answer:

False

Step-by-step explanation:

r × 100

= 0.500 × 100

= 50

Convert the decimal to percentage by multiplying by 100.

50 = 5,000%

False (5,000% ≠ 50)

Pablo and Alexei began arguing about who did better on their tests, but they couldn't decide who did better given that they took different tests. Pablo took a test in English and earned a 71.3, and Alexei took a test in Social Studies and earned a 67.5. Use the fact that all the students' test grades in the English class had a mean of 74.4 and a standard deviation of 11.4, and all the students' test grades in Social Studies had a mean of 66 and a standard deviation of 9.3 to answer the following questions. a) Calculate the z-score for Pablo's test grade. z=1 b) Calculate the z-score for Alexei's test grade. z=1 c) Which person did relatively better? Pablo Alexei They did equally well.

Answers

Pablo and Alexei performed equally well on their tests.

Step 1: Calculate the z-score for Pablo's test grade.

To calculate the z-score, we subtract the mean of the English class (74.4) from Pablo's test grade (71.3) and divide it by the standard deviation of the English class (11.4).

Z-score = (71.3 - 74.4) / 11.4 = -0.27

Step 2: Calculate the z-score for Alexei's test grade.

Similarly, we subtract the mean of the Social Studies class (66) from Alexei's test grade (67.5) and divide it by the standard deviation of the Social Studies class (9.3).

Z-score = (67.5 - 66) / 9.3 = 0.16

Step 3: Compare the z-scores.

Comparing the calculated z-scores, we find that Pablo's z-score is approximately -0.27, and Alexei's z-score is approximately 0.16.

Since both z-scores are relatively close to zero and have similar magnitudes, it indicates that both Pablo and Alexei performed similarly compared to the average scores of their respective classes.

Therefore, based on the z-scores, we can conclude that Pablo and Alexei did equally well on their tests.

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Listed below are measured amounts of caffeine (mg per 12 oz of drink) obtained in one can from each of 20 brands (7-UP, A&W Root Beer, Cherry Coke, Tab, etc.).
0, 0, 34, 34, 34, 45, 41, 51, 55, 36, 47, 41, 0, 34, 53, 54, 38, 0, 41, 47
What important feature of the data is not revealed by any of the measures of center? Choose those that are most appropriate.
Group of answer choices
Skewness to one side
Multimodal feature in the data
Possible outliers
Depth of dispersion
All of the above.
None of the above.

Answers

The important feature of the data that is not revealed by any of the measures of center is the possibility of outliers. The correct answer is C.

Outliers are extreme values that are significantly different from the majority of the data. In this case, the values 0, 45, 51, 55, and 54 could potentially be outliers as they are noticeably different from the other values in the data set. Outliers can affect the measures of center, such as the mean, but they are not captured by the mean, median, or mode alone.

Therefore, the correct answer is "Possible outliers." The correct answer is C.

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A vending machine at City Airport dispenses hot coffee, hot chocolate, or hot tea, in a constant service time of 20 seconds. Customers arrive at the vending machine at a mean rate of 60 per hour (Poisson distributed). Determine the operating characteristics of this system.
Which type of queuing problem is this?
a) Finite Population
b) Undefined Service Rate
c) Multi-Server
d) Finite Que
e) Constant Service Rate
f) Simple Single Server

Answers

The given problem involves Simple Single Server queuing model.In the given problem, a vending machine at City Airport dispenses hot coffee, hot chocolate, or hot tea, in a constant service time of 20 seconds. Customers arrive at the vending machine at a mean rate of 60 per hour (Poisson distributed).

The operating characteristics of this system can be determined by using the following formulas:Average Number of Customers in the System, L = λWwhere, λ= Average arrival rateW= Average waiting timeAverage Waiting Time in the System, W = L/ λProbability of Zero Customers in the System, P0 = 1 - λ/μwhere, μ= Service rateThe given problem can be solved as follows:Given that, λ = 60 per hourSo, the average arrival rate is λ = 60/hour. We know that the exponential distribution (which is a Poisson process) governs the time between arrivals. Therefore, the mean time between arrivals is 1/λ = 1/60 hours. Therefore, the rate of customer arrivals can be calculated as:μ = 1/20 secondsTherefore, the rate of service is μ = 3/hour.

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A binomial experiment has 10 trials with probability of success 0.8 on each trial. What is the probability of less than two successes?

Answers

The probability of less than two successes is approximately 0.0000082944.


To calculate the probability of less than two successes in a binomial experiment with 10 trials and a probability of success of 0.8 on each trial, we can use the binomial probability formula. The probability can be found by summing the probabilities of getting 0 and 1 success in the 10 trials.

In a binomial experiment, the probability of getting exactly x successes in n trials, where the probability of success on each trial is p, is given by the binomial probability formula:

P(x) = C(n, x) * p^x * (1 - p)^(n - x)

In this case, we want to find the probability of less than two successes, which means we need to calculate P(0) + P(1). Since we have 10 trials and a probability of success of 0.8, the calculations are as follows:

P(0) = C(10, 0) * 0.8^0 * (1 - 0.8)^(10 - 0)

    = 1 * 1 * 0.2^10

    = 0.2^10

P(1) = C(10, 1) * 0.8^1 * (1 - 0.8)^(10 - 1)

    = 10 * 0.8 * 0.2^9

    = 10 * 0.8 * 0.2^9

Finally, we add the probabilities:

P(less than two successes) = P(0) + P(1)

                          = 0.2^10 + 10 * 0.8 * 0.2^9

P(less than two successes) = 0.2^10 + 10 * 0.8 * 0.2^9

                          = 0.0000001024 + 10 * 0.8 * 0.000001024

                          = 0.0000001024 + 0.000008192

                          ≈ 0.0000082944

Therefore, the probability of less than two successes is approximately 0.0000082944.


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9.A confusion matrix is a matrix with the columns labeled with actual classes and the rows labeled with predicted classes. The values in the matrix represent the fraction of instances that fall within each combination of categories.
Select one:
True
False
10. Referring to inverse document frequency, the more documents in which a term occurs, the more significant it likely is to be to the documents it does occur in.
Select one:
True
False
11. Which of the following is always true?
a.P(AB) = P(A)/(P(B) + P(A))
b. P(AB) = P(A)P(A|B)
c. P(AB) = P(A)P(B|A)
d. P(AB) = P(A)P(B)
12. Good data journalism employs methods from this course to engage and involve readers to discover knowledge in data.
Select one:
True
False

Answers

9. False A confusion matrix is a matrix with the columns labeled with actual classes and the rows labeled with predicted classes.

10. True  the more documents in which a term occurs, the more significant it likely is to be to the documents it does occur in.

11. c. P(AB) = P(A)P(B|A)

12. True Good data journalism employs methods from this course to engage and involve readers to discover knowledge in data.

9. False. The statement is incorrect. In a confusion matrix, the columns are labeled with predicted classes, and the rows are labeled with actual classes. The values in the matrix represent the counts or frequencies of instances that fall within each combination of predicted and actual classes, not fractions.

10. True. Referring to inverse document frequency (IDF), the more documents in which a term occurs, the less significant or informative it is likely to be to the documents it does occur in. IDF is a measure used in natural language processing and information retrieval to quantify the importance of a term in a collection of documents. Terms that occur in fewer documents are considered more significant and receive higher IDF scores.

11. c. P(AB) = P(A)P(B|A). This statement represents the multiplication rule of probability, which states that the probability of two events A and B occurring together (denoted as P(AB)) is equal to the probability of event A occurring (P(A)) multiplied by the conditional probability of event B occurring given that event A has occurred (P(B|A)).

12. True. Good data journalism often incorporates methods from data analysis and visualization to engage and involve readers in the process of exploring and understanding data. By presenting data in a compelling and interactive way, data journalism can help readers discover insights and knowledge hidden within the data.

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Find the general solution of Euler type equation r²y" - ry - y = x + 1. Hint: look for solutions of the type y = for the homogeneous one and then find a particular solution.

Answers

To find the general solution of the Euler-type equation r²y" - ry - y = x + 1, we can first solve the homogeneous equation r²y" - ry - y = 0 by assuming a solution of the form y = xrⁿ.

Then, we find the values of n that satisfy the characteristic equation r² - r - 1 = 0 to obtain the homogeneous solutions. Next, we look for a particular solution of the non-homogeneous equation by assuming a solution of the form y = Ax + B. Finally, combining the homogeneous solutions and the particular solution gives us the general solution to the given equation.

The homogeneous equation r²y" - ry - y = 0 can be solved by assuming a solution of the form y = xrⁿ, where r is a constant. Substituting this into the equation gives us r²(xrⁿ)" - r(xrⁿ) - xrⁿ = 0. Simplifying this expression and factoring out xrⁿ, we get r²n(n - 1)xrⁿ⁻² - rxrⁿ - xrⁿ = 0. Dividing both sides by xrⁿ⁻² and simplifying further gives us the characteristic equation r² - r - 1 = 0.

Solving the characteristic equation r² - r - 1 = 0, we find the values of r that satisfy it. Let's assume the solutions are r₁ and r₂. Then the homogeneous solutions to the equation r²y" - ry - y = 0 are y₁ = xⁿ¹r₁ and y₂ = xⁿ²r₂, where n₁ and n₂ are determined by the values of r₁ and r₂.

To find a particular solution of the non-homogeneous equation r²y" - ry - y = x + 1, we assume a solution of the form y = Ax + B. Substituting this into the equation gives us r²(0) - r(Ax + B) - (Ax + B) = x + 1. By comparing the coefficients of x and the constant terms, we can solve for the values of A and B.

Finally, the general solution to the given equation is given by y = C₁xⁿ¹r₁ + C₂xⁿ²r₂ + Ax + B, where C₁ and C₂ are arbitrary constants and A and B are determined by the particular solution.

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If log(x-3) = 2, find x. A. 103 B. 97 C. 7 D. 13 4. Which of the following shows the graph of y = log x? A. B. C. D. fee for your of (1, 0) (1, 0) (0, 1) (0, 1) X 1 ažb³ 7. (a) Simplify3 a 2b4 (b) Solve 2x-1 = 64 and give the answer with positive indices. DFS Foundation Mathematics I (ITE3705) 8. It is given that y varies directly as x². When x = 4, y = 64. (a) Express y in terms of x. (b) Find y if x =3. (c) Find x if y=100. 10. The table shows the test results of 6 students in DFS Mathematics. Draw a bar chart for the table. Students Peter Ann May John Joe Marks 15 32 38 21 27 Sam 12 (7 marks) 11. The profit (SP) of selling a mobile phone is partly constant and partly varies directly as the number of phones (n) sold. When 20 phones were sold, the profit will be $3,000. When 25 phones were sold, the profit will be $5,400. (a) Express P in terms of n. (9 marks) (b) Find the profit when 40 phones were sold. (3 marks) (c) Find number of phones were sold if the targets profit is $23,640?

Answers

To find x in the equation log(x-3) = 2, we can rewrite the equation as 10^2 = x - 3. Solving for x gives x = 103. Therefore, option A is the correct answer.

The graph of y = log x is represented by option C. It shows a curve that passes through the point (1, 0) and approaches positive infinity as x increases.

(a) Simplifying 3a^2b^4 gives 3a^2b^4.

(b) Solving 2x - 1 = 64 yields x = 33.

(c) Expressing y in terms of x, we have y = kx², where k is a constant. Substituting x = 4 and y = 64 gives 64 = k * 4², leading to k = 4. Thus, y = 4x².

(d) Substituting x = 3 into the expression y = 4x² gives y = 4 * 3² = 36.

(e) Solving y = 100 for x, we have 100 = 4x², which results in x = ±5.

The bar chart for the test results of 6 students in DFS Mathematics is not provided. However, it should display the names of the students on the x-axis and their corresponding marks on the y-axis, with bars representing the height of each student's mark.

(a) Expressing P (profit) in terms of n (number of phones sold), we can write P = c + kn, where c is the constant part of the profit and k is the rate of change.

(b) Substituting n = 40 into the expression P = c + kn and using the given information, we can calculate the profit.

(c) To find the number of phones sold if the target profit is $23,640, we can set P = 23,640 and solve for n using the given equation.

The first two questions involve solving equations. In the first question, we can solve for x by converting the logarithmic equation to an exponential form. By comparing the equation to 10^2 = x - 3, we can determine that x = 103. The second question asks us to identify the graph that represents y = log x, which is option C based on the given description.

The next set of questions involves simplifying algebraic expressions, solving equations, and working with direct variation. In question 7a, the expression 3a^2b^4 is already simplified. In question 7b, we solve the equation 2x - 1 = 64 and find x = 33. In question 8, we express y in terms of x and find the value of y for given values of x. In question 10, a bar chart is required to represent the test results of 6 students. Unfortunately, the specific details and data for the chart are not provided. In question 11, we express the profit P as a function of the number of phones sold, solve for profit values given a certain number of phones sold, and find the number of phones sold for a target profit.

Overall, the questions involve a mix of algebraic manipulations, problem-solving, and data representation.

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Solve the boundary value problem u = 2x, uz (0,y) = e, u(0, y) = ³.

Answers

To solve the boundary value problem with the given conditions u = 2x, uₓ(0,y) = e, and u(0, y) = ³, we can integrate the partial derivatives with respect to x and apply the given boundary conditions to determine the solution.

The given boundary value problem consists of the equation u = 2x and the boundary conditions uₓ(0, y) = e and u(0, y) = ³.

Integrating the equation u = 2x with respect to x, we get u = x² + C(y), where C(y) is the constant of integration with respect to y.

Differentiating u = x² + C(y) with respect to x, we obtain uₓ = 2x + C'(y), where C'(y) represents the derivative of C(y) with respect to y.

Applying the boundary condition uₓ(0, y) = e, we have 2(0) + C'(y) = e. Therefore, C'(y) = e.

Integrating C'(y) = e with respect to y, we find C(y) = ey + K, where K is the constant of integration with respect to y.

Substituting C(y) = ey + K back into the expression for u, we have u = x² + ey + K.

Applying the boundary condition u(0, y) = ³, we get 0² + ey + K = ³. Hence, ey + K = 3.

Solving for K, we have K = 3 - ey.

Substituting K = 3 - ey back into the expression for u, we obtain u = x² + ey + (3 - ey) = x² + 3.

Therefore, the solution to the boundary value problem is u = x² + 3.

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A sample of size n=88 is drawn from a normal population whose standard deviation is σ=8.7. The sample mean is x
ˉ
=40.53. Part 1 of 2 (a) Construct a 98% confidence interval for μ. Round the answer to at least two decimal places. A 98% confidence interval for the mean is Part 2 of 2 (b) If the population were not approximately normal, would the confidence interval constructed in part (a) be valid? Explain. The confidence interval constructed in part (a) be valid since the sample size large.

Answers

(a) A 98% confidence interval for the mean is The formula for finding the confidence interval for the mean is given by;[tex]CI = \bar{x} ± Z_{α/2} \frac{σ}{\sqrt{n}}[/tex]Where;[tex]\bar{x}[/tex] = sample mean[tex]Z_{α/2}[/tex] = critical value[tex]σ[/tex] = standard deviation[tex]n[/tex] = sample size.  

At a 98% confidence level, the critical value (Z) will be 2.33 (using z-tables). Therefore, substituting the values into the formula above gives:[tex]CI = 40.53 ± 2.33\left(\frac{8.7}{\sqrt{88}}\right)[/tex][tex]CI = 40.53 ± 2.33(0.926)[/tex][tex]CI = 40.53 ± 2.154[/tex][tex]CI = (38.38, 42.68)[/tex]Therefore, the 98% confidence interval for μ is (38.38, 42.68).(b)The confidence interval constructed in part (a) will be valid even if the population is not approximately normal. This is because the sample size of n = 88 is greater than 30. The Central Limit Theorem (CLT) states that when the sample size is large enough (n > 30), the sampling distribution of the sample mean is approximately normal, regardless of the population distribution.      

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For each situation, sketch what you think the histogram of the
population data should look like and explain why you think it
should be that way. (That is, if we collect the data for everyone
in the po

Answers

Histograms are a chart representing the distribution of numerical data. They are an estimate of the population and its distribution. A histogram shows the frequency distribution of a variable. It is a visual representation of the data.

Histograms are useful tools for understanding population data. They give us a sense of the shape, center, and spread of the data. Histograms are commonly used to describe large amounts of data that are collected over a long period of time. They help us understand the shape of the data and the range of values that the data spans. The data is grouped into different ranges or bins. Each bin represents a different value range. The height of each bin corresponds to the number of data points that fall into that bin. The width of each bin is determined by the range of values that it represents. The histogram of population data will depend on the situation. For example, if we are collecting data on the height of the population, the histogram will likely be a bell curve shape. This is because most people fall in the middle range of heights, and fewer people fall into the extreme height ranges. The histogram will be centered around the mean height of the population. If we are collecting data on the age of the population, the histogram will be different. It will likely be a positively skewed distribution, with the majority of the population falling into the younger age range and fewer people falling into the older age ranges. This is because people tend to die off as they get older. The histogram will be centered around the median age of the population.

In conclusion, the histogram of population data will depend on the situation. It will be different for different variables. Histograms are useful tools for understanding the distribution of data. They give us a sense of the shape, center, and spread of the data.

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Find the zero(s) of the given functions and state the multiplicity of each. 1) g(x) = (x-3)(x+2)³(x - 5)²

Answers

the zeros of the function g(x) = (x - 3)(x + 2)³(x - 5)² are x = 3 with multiplicity 1, x = -2 with multiplicity 3, and x = 5 with multiplicity 2.

The given function is g(x) = (x - 3)(x + 2)³(x - 5)². To find the zeros of the function, we set g(x) equal to zero and solve for x. The zeros of the function are the values of x for which g(x) equals zero.

By inspecting the factors of the function, we can determine the zeros and their multiplicities:

Zero x = 3:

The factor (x - 3) equals zero when x = 3. So, the zero x = 3 has a multiplicity of 1.

Zero x = -2:

The factor (x + 2) equals zero when x = -2. So, the zero x = -2 has a multiplicity of 3.

Zero x = 5:

The factor (x - 5) equals zero when x = 5. So, the zero x = 5 has a multiplicity of 2.

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Based on a new survey, farm-hand workers in the United States who were employed on a farm or ranch earned an average of $38,230 a year in 2010. Suppose an economist wants to check whether this mean has changed since 2010. State the null and alternative hypothesis (just typing out the word mu is ok). Include a sentence of a verbal explanation of the null and alternative. Also state is this is a one or two-tailed test and why.

Answers

The null and alternative hypotheses regarding whether the mean farm-hand worker's pay has changed since 2010 are:

H0: µ = $38,230 ; Ha: µ ≠ $38,230

Based on a new survey, farm-hand workers in the United States who were employed on a farm or ranch earned an average of $38,230 a year in 2010.

Suppose an economist wants to check whether this mean has changed since 2010.

The null and alternative hypotheses regarding whether the mean farm-hand worker's pay has changed since 2010 are:

H0: µ = $38,230

Ha: µ ≠ $38,230

Null hypothesis (H0): This states that there is no statistically significant difference between the farm-hand worker's pay in 2010 and their pay now.

It is assumed that the mean farm-hand worker's pay is still $38,230.

Alternative hypothesis (Ha): This states that there is a statistically significant difference between the farm-hand worker's pay in 2010 and their pay now. It is assumed that the mean farm-hand worker's pay is not equal to $38,230.

The null hypothesis is a two-tailed test. The reason is that we need to check if the mean is significantly different from the average pay either in the negative direction or in the positive direction.

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• Problem 1. Let l > 0 and c/0. Let v continuous div = c²8² v Sv: [0, ] × [0, [infinity]) → R : v(0, t) - 0 (dv) (l, t) = 0 Show that S is a vector subspace of the function space C([0, 1] x [0, [infinity])).

Answers

S satisfies all three conditions, we can conclude that S is a vector subspace of the function space C([0, 1] × [0, ∞)).

To show that S is a vector subspace of the function space C([0, 1] × [0, ∞)), we need to verify three conditions:

1. S is closed under vector addition.

2. S is closed under scalar multiplication.

3. S contains the zero vector.

Let's go through each condition:

1. S is closed under vector addition:

  Let f, g be functions in S. We need to show that f + g is also in S.

 

  To show this, we need to prove that (f + g)(0, t) = 0 and ∂v/∂t(l, t) = 0.

 

  Since f and g are in S, we have f(0, t) = 0 and ∂f/∂t(l, t) = 0, and similarly for g.

 

  Now, consider (f + g)(0, t) = f(0, t) + g(0, t) = 0 + 0 = 0.

  Also, (∂(f + g)/∂t)(l, t) = (∂f/∂t + ∂g/∂t)(l, t) = ∂f/∂t(l, t) + ∂g/∂t(l, t) = 0 + 0 = 0.

 

  Hence, (f + g) satisfies the conditions of S, so S is closed under vector addition.

 

2. S is closed under scalar multiplication:

  Let f be a function in S and c be a scalar. We need to show that c * f is also in S.

 

  To show this, we need to prove that (c * f)(0, t) = 0 and ∂v/∂t(l, t) = 0.

 

  Since f is in S, we have f(0, t) = 0 and ∂f/∂t(l, t) = 0.

 

  Now, consider (c * f)(0, t) = c * f(0, t) = c * 0 = 0.

  Also, (∂(c * f)/∂t)(l, t) = c * (∂f/∂t)(l, t) = c * 0 = 0.

 

  Hence, (c * f) satisfies the conditions of S, so S is closed under scalar multiplication.

 

3. S contains the zero vector:

  The zero vector is the function v0(x, t) = 0 for all x in [0, 1] and t in [0, ∞).

  Clearly, v0(0, t) = 0 and ∂v0/∂t(l, t) = 0, so v0 is in S.

 

  Hence, S contains the zero vector.

Since S satisfies all three conditions, we can conclude that S is a vector subspace of the function space C([0, 1] × [0, ∞)).

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Using variation of parameters, find the particular solution of the differential equation x²y" - xy + y = 6x ln x, x > 0 if the solution to the auxiliary homogeneous d.e. is Yc = C₁x + c₂a ln(x). = Ур Enter your answer here

Answers

To find the particular solution of the differential equation x²y" - xy + y = 6x ln x using variation of parameters, we first need to find the Wronskian of the homogeneous solutions.

The homogeneous solutions are Yc = C₁x + C₂ ln(x), where C₁ and C₂ are constants. The Wronskian, denoted as W(x), is given by the determinant: W(x) = |x ln(x)|= |1 1/x |. Calculating the determinant, we get: W(x) = x(1/x) - ln(x)(1) = 1 - ln(x). Next, we find the particular solution using the variation of parameters formula: yp = -Y₁ ∫(Y₂ * g(x)) / W(x) dx + Y₂ ∫(Y₁ * g(x)) / W(x) dx. where Y₁ and Y₂ are the homogeneous solutions, and g(x) is the non-homogeneous term (6x ln x). Substituting the values, we have: yp = -(C₁x + C₂ ln(x)) ∫((C₁x + C₂ ln(x)) * 6x ln x) / (1 - ln(x)) dx + (C₁x + C₂ ln(x)) ∫(x * 6x ln x) / (1 - ln(x)) dx. Integrating these expressions will yield the particular solution. However, due to the complexity of the integrals involved, it is not possible to provide an exact expression in this format.

Therefore, the particular solution using variation of parameters is given by integrating the above expressions and simplifying.

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Spread of the student performance on assignment1 is higher for class A than class B. If we choose a student randomly from each class, then which student has a higher probability of taking values that are far away from the mean or expected value?
I have trouble understanding this question. What the correct answer is class A or class B?

Answers

Based on the given information that the spread of student performance on assignment1 is higher for class A than class B, the student from class A has a higher probability of taking values that are far away from the mean or expected value.

The spread of data refers to how much the individual values deviate from the mean or expected value. When the spread is higher, it means that the data points are more widely dispersed or varied. Therefore, in the context of student performance on assignment1, if the spread is higher in class A compared to class B, it implies that the individual student scores in class A are more likely to be farther away from the mean or expected value compared to class B.

In other words, class A may have a wider range of performance levels, including both higher and lower scores, compared to class B. This suggests that if a student is randomly chosen from each class, the student from class A is more likely to have a score that is far from the average or expected score of the class.

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1. a. For the standard normal distribution, find the value z 0

satisfying each of the following conditions. a) P(−z 0


)=0.3544 b. A normal random variable x has a mean 8 and an unknown standard deviation σ. The probability that x is less than 4 is 0.0708. Find σ.

Answers

In the given problem, we need to find the value of z satisfying specific conditions for the standard normal distribution and determine the unknown standard deviation σ for a normal random variable with a known mean and given probability.

a) To find the value of z satisfying the condition P(−z₀) = 0.3544, we can use a standard normal distribution table or a calculator. Looking up the value in the table, we find that z₀ ≈ -0.358.

b) To find the unknown standard deviation σ when the mean is 8 and the probability that x is less than 4 is 0.0708, we need to use the standard normal distribution. We can calculate the z-score for x = 4 using the formula z = (x - μ) / σ, where μ is the mean and σ is the standard deviation. Rearranging the formula, we have σ = (x - μ) / z. Substituting the given values, we get σ = (4 - 8) / z. Using the z-score associated with a cumulative probability of 0.0708 (from the standard normal distribution table or calculator), we can find the corresponding value of z and then calculate σ.

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Given that g(a) = 2a − 1 and h(a) = 3a − 3 determine (g × h)(−4) 135 11 2 2 -21

Answers

To find (g × h)(−4), we evaluate g(−4) = -9 and h(−4) = -15. Multiplying them gives (g × h)(−4) = 135.

To find the value of (g × h)(−4), we first need to evaluate g(−4) and h(−4), and then multiply the results.

Let's start by evaluating g(−4):

g(a) = 2a − 1

g(−4) = 2(-4) − 1

       = -8 - 1

       = -9

Next, we evaluate h(−4):

h(a) = 3a − 3

h(−4) = 3(-4) − 3

       = -12 - 3

       = -15

Finally, we multiply g(−4) and h(−4):

(g × h)(−4) = g(−4) × h(−4)

            = (-9) × (-15)

            = 135

Therefore, (g × h)(−4) equals 135.

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Find a real-life application of integration: 1- Only Two students in the group. 2- Use coding to produce the application (Optional).

Answers

One real-life application of integration is in calculating the area under a curve, which can be used in fields like physics to determine displacement, velocity, or acceleration from position-time graphs.

Integration has various real-life applications across different fields. One example is in physics, where integration is used to calculate the area under a curve representing a velocity-time graph. By integrating the function representing velocity with respect to time, we can determine the displacement of an object.

This concept is fundamental in calculating the distance traveled or position of an object over a given time interval. Real-life scenarios where this application is used include motion analysis, predicting trajectories, and understanding the relationship between velocity and position.

In coding, various numerical integration techniques, such as the trapezoidal rule or Simpson's rule, can be implemented to approximate the area under a curve and provide accurate results for real-world calculations.

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A study shows that 8,657 out of 28,866 UUM students own a motorcycle. Suppose from a sample of 150 students selected, 57 of them own motorcycles. Compute the sample proportion of those that own motorcycles.

Answers

The sample proportion of UUM students who own motorcycles, based on a sample of 150 students, is 0.38 or 38%.

In the given study, it is stated that out of a total of 28,866 UUM students, 8,657 own a motorcycle. This implies that the population proportion of UUM students who own motorcycles is 8,657/28,866 ≈ 0.299 or 29.9%.

To compute the sample proportion, we can use the information from the sample of 150 students, where 57 of them own motorcycles. The sample proportion is calculated by dividing the number of students who own motorcycles in the sample by the total sample size. In this case, the sample proportion is 57/150 ≈ 0.38 or 38%.

The sample proportion is an estimate of the population proportion, providing an indication of the proportion of UUM students who own motorcycles based on the sample data. It suggests that approximately 38% of UUM students in the given sample own motorcycles. However, it's important to note that this is an estimate, and the true population proportion may differ slightly.

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Other Questions
TRUE / FALSE. "The California Gold Rush and mining in California more generallyduring this period relied little on California Indian labor. a. Explain the definition of interim payment.b. All contents in a contract describes rights and obligations of parties under the contract. Those contents can be in two types of term, either express or implied term. Explain both implied and express term, with example. Paul is in the armed services and asks his father George to handle his household affairs while he is deployed in the Mid-East. There is no further discussion and there is no writing. The lot next to Paul's house goes up for sale and George is confident that Paul would want him to buy it. George signs a contract to purchase the lot as agent for Paul. When he gets back, Paul is angry about George's decision and wants to get out of the contract. What legal arguments would Paul have?A.George did not have authority to enter into the contract pursuant to the equal dignity rule.B.George did not have actual authority to enter into the contract.C.George did not have implied authority to enter into the contract.D.All of the above. Suppose I want to know something about the study habits of undergraduate college students. Icollect a random sample of 200 students and find that they spend 12 hours per week studying, onaverage, with a standard deviation of 5 hours. I am curious how their social lives might be associatedwith their studying behavior, so I ask the students in my sample how many other students at theiruniversity they consider "close friends." The sample produces an average of 6 close friends with astandard deviation of 2. Please use this information to answer the following questions. The correlationbetween these two variables is -.40.1. Assume that "Hours spent studying" is the Y variable and "Close friends" is the X variable.Calculate the regression coefficient (i.e., the slope) and wrap words around your results. What,exactly, does this regression coefficient tell you?2. What would the value of the standardized regression coefficient be in this problem? How do youknow?3. Calculate the intercept and wrap words around your result.4. If you know that somebody studied had 10 close friends, how many hours per week would youexpect her to study?5. What, exactly, is a residual (when talking about regression)?6. Regression is essentially a matter of drawing a straight line through a set of data, and the linehas a slope and an intercept. In regression, how is it decided where the line should be drawn? Inother words, explain the concept of least squares to me.7. Now suppose that I add a second predictor variable to the regression model: Hours per weekspent working for money. And suppose that the correlation between the hours spent workingand hours spent studying is -.50. The correlation between the two predictor variables (numberof close friends and hours spent working for money) is -.30.a. What effect do you think the addition of this second predictor variable will have on theoverall amount of variance explained (R2 ) in the dependent variable? Why?b. What effect do you think the addition of this second predictor variable will have on thestrength of the regression coefficient for the first predictor variable, compared to whenonly the first predictor variable was in the regression model? Why? Assuming no budget constraints, maximization of total utility when choosing the amounts of two goods to purchase occurs when the ratios of marginal utility divided by price are equal for both goods. True False Imagine that you are an international business consultant to a fictitious company (make up your own product or products or service) that has decided to explore the possibilities of expansion into at least two countries.Create a 45-page paper in which you justify your assertions for each of the following:Develop a brief overview of the fictitious company including its product(s).Choose at least two different foreign countries where the company would globalize the product or their products, and analyze the following objectives:Develop a brief profile of the countries that you have chosen.Expected effects and driving forces as a result of the companys globalization plan.Successful strategies to enter the global market for the different foreign countries that you selected.Comparative analysis between the companys domestic and global environments.External factors or environments of the selected countries (political, economic, technological, legal, and others) which could benefit or discourage international business.Investigate the key factors that you would need to understand to guide an effective pricing strategy for your product or service, based on your foreign currencies analysis for your selected countries.Comparative analysis between international trade, foreign direct investment, and global joint ventures. Explain which one of these models would you choose.Better practices to look for international business opportunities for your company and for your product(s). As many of you are aware, due to measures to combat Covid, many governments incurred steep deficits which added to the debt. Some governments are now contemplating tax increases to help reduce the deficit and/or debt. Possible ways of increasing revenue is to increase income taxes and/or sales taxes such as the GST/HST. Sources of income that taxes are paid on include labour (work) as well as business profits and investment earnings. Assuming that taxes are to be raised, which tax increase would be least detrimental to long term economic growth, a GST/HST increase or an increase in income tax? Assume that either of the increases would be revenue neutral, i.e., the federal government would take in the same amount of revenue with either tax that is raised. Consider the following hypothesis test.H0: = 20Ha: 20A sample of 200 items will be taken and the population standard deviation is = 10.Use = .05. Compute the probability of making a Type II error if the populationmean is:a. = 18.0b. = 22.5c. = 21.0 Daly Publishing Corporation recently purchased a truck for $43,000. Under MACRS, the first years depreciation was $6,000. The truck drivers salary in the first year of operation was $8,600. The companys tax rate is 30 percent.Required:1-a. Calculate the after-tax cash outflow for the acquisition cost and the salary expense.1-b. Calculate the reduced cash outflow for taxes in the first year due to the depreciation. Presented below are two independent situations.a. On January 6, Brumbaugh Co. sells merchandise on account to Pryor Inc. for $7,000, terms 2/10, n/30. On January 16. Pryor Inc. pays the amount due.Prepare the entries on Brumbaugh's books to record the sale and related collection.b. On January 10, Andrew Farley uses his Paltrow Co. credit card to purchase merchandise from Paltrow Co. for $9,000. On February 10, Farley is billed for the amount due of $9,000. On February 12, Farley pays $5,000 on the balance due. On March 10, Farley is billed for the amount due, including interest at 1 percentage per month on the unpaid balance as of February 12. Prepare the entries on Paltrow Co.'s books related to the transactions that occurred on January 10, February 12, and March 10. "Khosrowshahi met the company's staff-run clubs that support people from different backgrounds." 3.1 Outline Uber's initiatives which aim to promote diversity. In addition, discuss the various approaches that can be adopted in an attempt to achieve effective workforce diversity. Using contribution margin format income statement to measure the magnitude of operating leverageThe following income statement was drawn from the records of Butler Company, a merchandising firm:BUTLER COMPANYIncome StatementFor the Year Ended December 31, 2014,Sales revenue (2,000 units $275)$550,000Cost of goods sold (2,000 units $146)(292,000)Gross margin258,000Sales commissions (10% of sales)(55,000)Administrative salaries expense(80,000)Advertising expense(38,000)Depreciation expense(50,000)Shipping and handling expenses (2,000 units $1.50)(3,000)Net income$32,000Requireda. Reconstruct the income statement using the contribution margin format.b. Calculate the magnitude of operating leverage. (Round your answer to 2 decimal places.)c. Use the measure of operating leverage to determine the amount of net income Butler will earn if sales increase by 10 percent. (Do not round intermediate calculations.) Discuss the noticeable and/or important effects that arise from the cancellation and reinforcing of waves and the different velocities of waves as they travel through different parts of the same material. Based on financial and opportunity costs, which of the following do you believe would be the wiser purchase? Vehicle 1: A three-year-old car with 45,000 miles, costing $15700 and requiring $585 of immediate repairs Vehicle 2: A five-year-old car with 62,000 miles, costing $9500 and requiring $960 of immediate repairs What is this solution?Illustration of Bilateral Mudarabah Bank Alrajhi provides SAR100,000 to Omar and profit sharing ratio is 70:30 If Loss is SAR 20,000 Bank Alrajhi If profit is SAR 40,000 bears the loss of SAR 20,000, Sapposa that the heights of adult women in the United states are nocmally tistnbuged with a mean of 64 inches and a standand deyiakiog of 2.5 inches. tucy is talter than 85% of the population of U.S. women. How tall (in inches) is Lucy? Carry your intermediate cornputations to at least four decimal places.Round your answer to vine deccimal flicke Directional plans ________.a) leave no room for interpretationb) are flexible general guidelinesc) are difficult to modifyd) must be short-term plans True or false - Stanley Park is an example of a preserved wilderness that has latigely been unmodified by humans over the past 100 years. a) True. b) False Adams Gyms Inc. owns athletic training facilities and camping grounds, which it leases to corporate clients, educational institutions, and other non-governmental organizations. The Rose Institute agrees to lease one of these athletic training facilities on the following terms:-The training facility comprises 7,200 acres in New York. The lessor owns only one training facility in this location.-The Rose Institute can use the training facility at its discretion over the lease term. Adams Gyms is prohibited from selling the facility during the lease term or terminating the lease agreement early.-The lease contract requires Adams Gyms Inc to upgrade the facility to comply with the American Disabilities Act. Subsequent lessees of the facility can benefit from these upgrades.-The lease term is 30 years with an option to renew for an additional 20 years. The Rose Institute is reasonably likely to renew. The useful life of this facility is 50 years.-The lessee does not automatically obtain ownership of the facility at the end of the lease term and the lessee is not given an option to purchase the facility at the end of the lease term.-Adams Gym Inc. will prove food catering services for four meals per day.-The present value of the sum of the lease payments is $12 million. The facility's fair market value is $13 million. The Rose Institute is responsible for repairing all damage to the facility or paying $150% of the cost of any repairsQuestion: Which provision of the lease contract implies that the customer has control over the use of the identified asset?A. The training facility comprises 7200 acres in New York. Adams Gym Inc. owns only one training facility in this location.B. Adams Gym Inc. will provide food catering services four meals per dayC. The Rose Institute can use the training facility at its discretion over the lease term. Adams Gyms Inc. is prohibited from selling the facility during the lease term or terminating the lease agreement early.D. The lease contract requires Adams Gyms Inc to update the facility to comply with the American Disabilities Act. Subsequent lessees of the facility can benefit from these upgrades. How might a leader use coaching to help increase ethicalbehavior among group members.300 words discussion