NORMAL distribution is what shape?
how many in 1st deviation
2nd deviation
3rd deviation

This is an incredibly long time, equivalent to about 111,000,000 years!  even with the ability to compute, store, and check for collisions at a rate of 2,000,000 instances per second, finding a collision in SHA3-256 with a probability of at least 1/100,000 is practically impossible.

The probability of finding a collision in a hash function with n-bit output, such as SHA3-256, is roughly proportional to the square root of the number of possible hash values is [tex]2^{(n/2)[/tex].

SHA3-256, n is 256, so the number of possible hash values is

[tex]2^{(256/2)} = 2^{128.[/tex]

Let t be the number of seconds we need to run the computation. In one second, we can compute 2,000,000 instances of SHA3-256.

In t seconds, we can compute 2,000,000t instances of SHA3-256.

The number of pairs of hash values that we can generate from 2,000,000t instances is

(2,000,000t choose 2) = (2,000,000t) × (2,000,000t - 1)/2.

To have a probability of at least 1/100,000 of finding a collision, we need the number of pairs of hash values to be at least 100,000 times the number of possible hash values, which is:

(2,000,000t) × (2,000,000t - 1)/2 >= 100,000 × 2¹²⁸

Simplifying and solving for t, we get:

[tex]t > = \sqrt{((100,000 \times 2^{128})/(2,000,000)^2 - 1/2,000,000)} \approx 3.52 \times 10^{15} seconds[/tex]

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The probability at least 1/100,000 of finding a collision is 2.12 x [tex]10^{29[/tex] seconds is approximately [tex]6.73 x 10^{21[/tex] years

In cryptography, a collision occurs when two different inputs produce the same hash output.

The probability of finding a collision increases as the number of inputs increases, and this is what we want to calculate.
Assuming we can compute, store, and check for collisions 2,000,000 instances of SHA-3 (SHA3-256) in one second, we can compute the number of possible inputs that can be hashed in a given time frame.

If we assume a year contains 31,536,000 seconds, then in one year we can compute:
2,000,000 * 31,536,000 = 63,072,000,000,000
That is 63.07 trillion inputs hashed in one year.
Next, we need to calculate the probability of finding a collision among all these inputs.

To do this, we can use the birthday paradox formula, which states that the probability of finding a collision in a set of n items is approximately [tex]n^2[/tex]/[tex]2^{(k+1)[/tex].

Where k is the number of bits in the hash output.

For SHA3-256, k = 256.
So, the probability of finding a collision in our set of hashed inputs is:
63,072,000,00 / 2(256+1) = 0.01266
This is an extremely small probability, which means it would take a very long time to find a collision with a probability of at least 1/100,000.

In fact, we would need to compute and store billions of times more hashes than what we can currently achieve in a year.
Therefore, to answer your question, we can say that even with the ability to compute, store, and check for collisions 2,000,000 instances of SHA-3 (SHA3-256) in one second, it would take an impractical amount of time to find a collision with a probability of at least 1/100,000.

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The eighth term, a8, of the arithmetic sequence is -17.

An arithmetic sequence is a sequence of the form a, a + d, a + 2d, a + 3d, a + 4d, … The number a is the first term, and d is the common difference of the. sequence.

To find the eighth term, a8, in an arithmetic sequence with the first term a1 = -3 and the common difference d = -2, we can use the formula for the nth term of an arithmetic sequence:

an = a1 + (n - 1) * d

Plugging in the given values, we have:

a8 = -3 + (8 - 1) * (-2)

= -3 + 7 * (-2)

= -3 - 14

= -17

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a) Zachary used random sampling to gather his data.

b) the percentage of red form each 5 sample are given as follows;

c) from the results in B we can state that 2 of the sample, red cars made up 10% of the observation, in another 2 sample, it was 15%. The sample with the highest observation of red cards is sample 2.

In statistics, a simple random sample is a subset of individuals picked at random from a larger collection, with all individuals having the same probability. It is the process of picking a sample at random.

Random sampling guarantees that the findings received from your sample are close to those obtained if the full population was surveyed.

See the attached table for the calculation.

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(a) The number 72% is a D. statistic.

(b) The unknown true percentage of American citizens who like ''real TV'' is a C. parameter.

It is related to statistics and parameters.

(a) The number 72% is a statistic because it represents a summary measure of the sample of individuals who participated in the phone-in poll.

A statistic is a numerical value calculated from a sample of data, and it is used to make inferences about the population from which the sample was drawn.

(b) The unknown true percentage of American citizens who like ''real TV'' is a parameter.

A parameter is a numerical characteristic of a population, such as a mean, proportion, or standard deviation, and it is typically unknown and estimated from sample data.

In this case, the percentage of all American citizens who like ''real TV'' is unknown and cannot be directly observed, so it is considered a parameter.

The phone-in poll only represents a sample of individuals who called in to the newspaper and cannot be used to estimate the parameter for the entire population.

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Each of the 8 student groups will need to raise $60.32 to help purchase the swing set.

The parent-teacher association needs to raise $482.56 to purchase the swing set after receiving a $200 donation. Each of the 8 student groups will need to raise an equal amount of $60.32 to reach the goal.

To calculate the amount each student group needs to raise, first subtract the $200 donation from the total cost of the swing set:

$682.56 - $200 = $482.56

Then, divide the remaining amount by the number of student groups:

$482.56 ÷ 8 = $60.32

Therefore, each of the 8 student groups will need to raise $60.32 to help purchase the swing set.

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The mean of this distribution is 1.601.

To find the mean of a discrete probability distribution, we need to multiply each outcome by its respective probability, and then add up these products. In this case, we have:

0(0.130) + 1(0.345) + 2(0.345) + 3(0.154) + 4(0.026)

= 0 + 0.345 + 0.69 + 0.462 + 0.104

= 1.601

Therefore, the mean of this distribution is 1.601. This value represents the expected value or average outcome if we were to repeat this experiment many times.

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Yes, the normal distribution can be used to approximate the probability of at least 92 people.

To determine if the normal distribution can be used to solve this problem, we need to check if the sample size is sufficiently large and if the sample proportion is not too close to 0 or 1.

The sample size is not given in the problem statement, but we can assume that it is large enough for the normal distribution to be a reasonable approximation. A general rule of thumb is that the normal distribution can be used if the sample size is at least 30.

The problem states that the probability of a random person recognizing the McDonald's brand name is 0.95. We can interpret this as the sample proportion (p-hat) being equal to 0.95. The normal distribution can be used to approximate the probability of at least 92 people recognizing the brand name if the following conditions are met:

Since we can assume that the sample size is large enough, and both np >= 10 and n(1-p) >= 10, we can use the normal distribution to approximate the probability of at least 92 people recognizing the McDonald's brand name.

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The binomial distribution can be approximated with a normal distribution when the sample size is large, typically when both np and n(1-p) are greater than or equal to 10, where n is the sample size and p is the probability of success. The correct answer is (c) large.

This is known as the normal approximation to the binomial distribution.

When the sample size is small or moderate, the normal approximation may not be appropriate, and the binomial distribution should be used to make inferences about the population proportion.

In such cases, the normal distribution may not accurately reflect the skewness and kurtosis present in the distribution of the binomial variable. As a rule of thumb, if np and n(1-p) are both less than 10, then the binomial distribution should be used instead of the normal approximation.

Therefore, the correct answer is (c) large.

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Answer:

x = 122°

Step-by-step explanation:

There is remote angle( non- adjecent angle) and their sum equal to the exterior angle .

Exterior angle is an angle formed from one side of the polygone and the extended side so

<A and <B are remot angle and <BCD is exterior angle .

And we write the equetion as

<A + <B = <BCD

58° + 64° = x°

122° = X°

so the exterior angle ( x ) measures 122° .

The actual price of the DVD is $15.00.

option C.

The actual price of the DVD before the sales tax is added is calculated as follows;

Let the actual price = T

When the 7 % tax is added, the new price becomes 1.07T

The value of the actual price is calculated as follows;

1.07T = $16.06

T =  $16.06 / 1.07

T = $15.00

Thus, the actual price of the DVD is equal to the original price of the DVD before tax.

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There are 863,040 ways to elect a president, vice president, secretary, and treasurer from a club of 32 members.

We can solve this problem using the concept of permutations.
To elect a president, vice president, secretary, and treasurer from a club of 32 members, we need to find the number of possible arrangements.

This can be calculated using the formula for permutations: nPr = n! / (n - r)!,

where n is the total number of members and r is the number of positions to fill.
In this case, n = 32 (total members) and r = 4 (president, vice president, secretary, and treasurer).
Calculate the factorials for n and (n - r)
32! = 32 × 31 × 30 × ... × 2 × 1
28! = 28 × 27 × 26 × ... × 2 × 1
Apply the permutation formula
32P4 = 32! / (32 - 4)!
32P4 = 32! / 28!
Calculate the final answer
32P4 = (32 × 31 × 30 × 29 × 28!) / 28!
32P4 = 32 × 31 × 30 × 29.
32P4 = 863,040.

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Quicksort is a popular sorting algorithm that works by partitioning the array into two sub-arrays, one with elements smaller than a chosen pivot element, and the other with elements greater than the pivot. It then recursively sorts these sub-arrays until the entire array is sorted.

To sort the given numbers using quicksort, we can start by choosing the last element, 28, as the pivot. We then partition the array as follows:

23, 20, 28, 34, 35, 43, 53, 87, 75, 94, 96, 75, 94

In this partition, all elements before 28 are smaller and all elements after 28 are greater. We then recursively apply quicksort to the left and right sub-arrays until the entire array is sorted.

For the left sub-array (23, 20, 28, 34, 35, 43, 53), we choose the last element, 53, as the pivot and partition as follows:

23, 20, 28, 34, 35, 43, 53

We then recursively apply quicksort to the left and right sub-arrays until the left sub-array contains only one element, at which point it is considered sorted. We then move on to the right sub-array (87, 75, 94, 96, 75, 94) and repeat the process.

The right sub-array can be partitioned using any element as the pivot, but we will choose the last element, 94. The partition is as follows:

75, 87, 75, 94, 94, 96

We then recursively apply quicksort to the left and right sub-arrays until they are sorted. Once both sub-arrays are sorted, we can combine them to get the final sorted array:

20, 23, 28, 34, 35, 43, 53, 75, 75, 87, 94, 94, 96

In summary, to sort the given numbers using quicksort, we choose a pivot, partition the array into two sub-arrays, and recursively apply quicksort to each sub-array until the entire array is sorted.

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It is not necessarily true that n(A - B) = n(A) - n(B) when A and B are sets.

Consider two sets, A = {1, 2, 3} and B = {1, 4}.

In this case, A - B = {2, 3}, n(A) = 3, n(B) = 2, and n(A - B) = 2. Therefore, n(A - B) ≠ n(A) - n(B).

In set theory, the difference of two sets A and B is defined as the set of elements in A that are not in B. The cardinality of a set is the number of elements it contains.

The equation n(A - B) = n(A) - n(B) is not always true, and there exist counterexamples where it does not hold. One such counterexample is A = {1, 2, 3} and B = {1, 4}. In this case, A - B = {2, 3}, n(A) = 3, n(B) = 2, and n(A - B) = 2. Thus, n(A - B) ≠ n(A) - n(B).

It is important to note that the equation n(A - B) = n(A) - n(B) holds only when every element in A - B is also in A and not in B. If this condition is not met, the equation does not hold.

Therefore, one must be cautious when applying this equation and ensure that all elements are properly accounted for.

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The equation is inconsistent, which means there is no valid solution for the average number of comic books (A). As a result, we cannot determine the number of comic books Patrick has based on the given information.

Let's denote the average number of comic books as "A".

Given that Sid has 19 comic books, we can use this information to determine the average number of comic books between Marvin and Patrick.

The total number of comic books among the three of them is:

19 (Sid's books) + A (Marvin's books) + A (Patrick's books)

According to the given information:

Marvin's number of comic books is 10 less than the average, which means Marvin has A - 10 books.

Patrick's number of comic books is 12 more than the average, which means Patrick has A + 12 books.

So, the total number of comic books among the three of them can be expressed as:

19 + (A - 10) + (A + 12)

Simplifying the expression:

2A + 1

Since we know the total number of comic books is the sum of the individual numbers, we have:

19 + (A - 10) + (A + 12) = 2A + 1

Simplifying further:

2A + 21 = 2A + 1

By subtracting 2A from both sides of the equation, we get:

21 = 1

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The equation in percentage given by, $2.21 + 8% tax = $2.3868 rounds to $2.4 to the nearest tenth.

Given an equation,

$2.21 + 8% tax = $2.3868

This is an equation which relates the cost including the percentage of tax.

When 2.21 is added to the tax amount, we get $2.3868.

2.21 + (0.08 × 2.21) = 2.3868

Here it is not mentioned up to what decimal we have to round the figure.

If 2.3868 is rounded to the nearest whole number, it becomes 2.

If 2.3868 is rounded to the tenth, it becomes 2.4.

If 2.3868 is rounded to the hundredth, it becomes 2.39.

Hence the rounded amount to the nearest tenth is $2.4.

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To find the length of side a in triangle ABC, we can use the law of sines:

a/sin(A) = b/sin(B)

We know that m∠A = 40, b = 8, and m∠C = 115. We can find m∠B by using the fact that the sum of the angles in a triangle is 180 degrees:

m∠A + m∠B + m∠C = 180

40 + m∠B + 115 = 180

m∠B = 25

Now we can plug in the values we know into the law of sines and solve for a:

a/sin(40) = 8/sin(25)

a = sin(40) * 8 / sin(25)

a ≈ 11.3 (rounded to the nearest tenth)

Therefore, the length of side a in triangle ABC is approximately 11.3 units, which corresponds to answer option G.

The length of JH in the similar triangle is 35.7 units.

Similar triangles are the triangles that have corresponding sides in proportion to each other and corresponding angles equal to each other.

Therefore, Triangle EFG is similar to triangle HIJ. The measure of side JH can be found as follows:

Using the proportions,

7 / 25 = 10 / JH

cross multiply

7JH = 25 × 10

7JH = 250

divide both sides by 7

JH = 250 / 7

JH = 35.7142857143

Therefore,

JH = 35.7 units

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Given 7x² + 3y² – 42x + 6y – 39 < 0, the graph that represents the above inequality is attached accordingly.

An inequality in mathematics is a relationship that makes a non-equal comparison between two integers or other mathematical expressions.

To determine what the graph of the inequality 7x ² + 3y² – 42x + 6y – 39 <  0 looks like, we can start by simplifying the equation and then analyzing its  properties.

First  factor out the coefficients of x² and y² ....the result is

7(x² - 6x) + 3(y² + 2y) - 39  < 0

Next, complete the square for x and y by adding and subtracting the square of half of the   coefficient of x and y, respectively

⇒ 7(x² - 6x + 9 - 9) +  3(y ² + 2y + 1 - 1) - 39 < 0

⇒ 7[(x - 3)² - 9]  + 3[(y + 1)² - 1] - 39 < 0

⇒   7(x - 3)² + 3(y + 1)² - 84 < 0

It can be noted  that the coefficients of (x - 3) ² and (y  + 1)² are positive. This  means that the equation represents an ellipse centered at (3,-1).

 Since the inequality is less than zero, we know that the points inside the   ellipse satisfy the inequality.

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Full Question:
See the attached.

The calculated value of the volume of the prism is 120 cubic cm

From the question, we have the following parameters that can be used in our computation:

The triangular based prism

By formula, we have the volume of the prism to be

Volume = base area  * Height

using the above as a guide, we have the following:

Base area = 1/2 * 4 * 5 = 10

Height = 12

substitute the known values in the above equation, so, we have the following representation

Volume = 10 * 12

Evaluate

Volume = 120

Hence, the volume of the prism is 120 cubic cm

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For a normal distribution, the likelihood (expressed as a percentage) that a random variable is within plus and minus two standard deviations of the mean is 95.44%.  The correct answer is option d.

This is also known as the "68-95-99.7 rule" or the "empirical rule." Specifically, approximately 68% of the data falls within one standard deviation of the mean, 95% of the data falls within two standard deviations of the mean, and 99.7% of the data falls within three standard deviations of the mean.

Therefore, in a normal distribution with a known mean and standard deviation, we can use this rule to estimate the percentage of data that falls within a certain range of values around the mean.

The correct answer is option d.

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Complete Question

For a normal distribution, whet is the likelihood (expressed as a percentage) that a random variable is within plus and minus two standard deviations of the mean?

a. 68.26%

b. 99.74%

c. 34.13%

d. 95.44%

Factor analysis, when originally developed, was assumed to be used to explore data to generate hypotheses and reveal underlying patterns or latent variables. This statistical technique is employed for reducing a large number of observed variables into a smaller set of factors, while retaining as much information as possible.

Factor analysis has two primary types: exploratory factor analysis (EFA) and confirmatory factor analysis (CFA). EFA is utilized to identify the potential structure and relationships among variables without imposing any preconceived notions. It seeks to uncover hidden dimensions or factors that might explain the correlations among the variables.

CFA, on the other hand, tests a predetermined factor structure based on prior research or theoretical assumptions. It examines whether the data fits the proposed model, allowing researchers to confirm or reject their hypotheses.

Overall, factor analysis has become a valuable tool in various fields, including psychology, sociology, and economics. By unveiling underlying factors, researchers can better understand complex data sets and draw more accurate conclusions from their studies.

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The drone's descent can be modeled by a linear function as the rate of descent is constant.

The slope-intercept definition of a linear function is given as follows:

y = mx + b.

In which:

m is the slope, representing the rate of change.

b is the intercept, representing the value of y when x = 0.

For this problem, we have that the drone descended 16 meters in 6 seconds, hence the slope m is given as follows:

m = -16/6 = 2.67 m/s.

As the slope is constant, a linear function can model the situation.

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The drone in the Example hovers at 16 meters for a few minutes before being

lowered at a constant rate. It reaches the ground after 6 seconds.

a. Why can the drone's descent be modeled by a linear function?

Answer:

72

Step-by-step explanation:

First of all, we need the numbers as a product of its prime numbers.

8 = 2×2×2

12 = 2×2×3

18 = 2×3×3

Now we can see that there is one 2 in all three numbers. And also two twos in 8,12 and two threes in 12,18. We need to group it and take it as one. The rest we take it individually each

So 2×2×2×3×3 = 8×9 = 72

The value of segment ST is determined as 14.5 in.

The value of length ST is calculated as follows;

ST² = TR x ( TR + QT)

From the diagram given, the length of the sides are as follows;

TR = 7 in

QT = 7 in + 23 in = 30 in

The value of segment ST is calculated as follows;

ST² = 7 x 30

ST² = 210

ST = √ ( 210 )

ST = 14.5 in

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The length ST on the tangent is 12.69 inches.

The Intersecting Secant-Tangent theorem states that  If a tangent and a secant are drawn to a circle from an outside point, then the square of the measure of the tangent segment is equal to the product of the measures of the secant segment and its external secant segment.

Therefore,

ST² = RT × RQ

Therefore,

RT = 7 inches

RQ = 23 inches

Hence,

ST² = 23 × 7

ST² = 161

ST = √161

ST = 12.6885775404

ST = 12.69 inches

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The probability of drawing 2 yellow markers and 2 red markers is approximately 0.2697.

To find the probability of drawing 2 yellow markers and 2 red markers, we need to calculate the total number of ways to draw 4 markers from the bag, as well as the number of ways to draw 2 yellow and 2 red markers.

The total number of ways to draw 4 markers from the bag is:

¹⁴C₄ = (14!)/(4!*(14-4)!) = 1001

This is because there are 14 markers in total, and we are choosing 4 of them.

To find the number of ways to draw 2 yellow and 2 red markers, we can use the combination formula again. The number of ways to choose 2 yellow markers from 4 yellow markers is:

⁴C₂ = (4!)/(2!*(4-2)!) = 6

Similarly, the number of ways to choose 2 red markers from 10 red markers is:

¹⁰C₂ = (10!)/(2!*(10-2)!) = 45

Therefore, the number of ways to draw 2 yellow and 2 red markers is:

6 * 45 = 270

Now we can find the probability of drawing 2 yellow and 2 red markers by dividing the number of ways to draw 2 yellow and 2 red markers by the total number of ways to draw 4 markers:

P(2 yellow and 2 red) = 270/1001 = 0.2697 (rounded to four decimal places)

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The probability of drawing 2 yellow marker and 2 red markers 15/1078

A probability is a number that reflects the chance or likelihood that a particular event will occur. The certainty an event will occur is 1 which is equivalent to 100%.

Probability = sample space / total outcome

for the first draw ;

probability of picking yellow = 2/14 = 1/7

second draw;

probability of picking yellow = 1/13

third draw;

probability of picking red = 10/12 = 5/6

fourth draw;

probability of picking red = 9/11

Probability of picking two yellow = 2/14 × 1/7 = 2/98 = 1/49

probability of picking two reds = 5/6 × 9/11 = 45/66 = 15/22

probability of picking 2 yellow and 2 red = 1/49 × 15/22 = 15/1078

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The probability that a randomly selected coffee drinker does not use sugar or cream is [tex]1 - p^2.[/tex]

To find the probability that a randomly selected coffee drinker does not use sugar or cream, we need to find the probability of the complement of the event (C or S).

That is, we need to find the probability of the coffee drinker not using cream and not using sugar.
We can use the formula P(not C and not S) = P(not C) * P(not S|not C),

where P(not C) is the probability of not using cream and P(not S|not C) is the conditional probability of not using sugar given that the coffee drinker does not use cream.
Since we do not have any information about the probabilities of using cream and sugar, we cannot find the exact probabilities.

However, we can assume that the probabilities are equal and use the complement rule, which states that P(not C or not S) = 1 - P(C and S).
Since we do not have any information about the joint probability of using cream and sugar, we can assume that the events C and S are independent. Therefore, P(C and S) = P(C) * P(S).
Assuming that P(C) = P(S) = p, we have P(not C or not S) = 1 - P(C and S) [tex]= 1 - p^2[/tex]

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Based on the results of the American Management Association/ePolicy Institute Survey on electronic monitoring and surveillance, companies reported that they had dismissed 30% of workers for misusing the Internet.

The survey conducted by the American Management Association/ePolicy Institute found that among the companies surveyed, 30% reported that they had dismissed employees for Internet misuse. This suggests that companies are taking Internet security seriously and are willing to take action against employees who violate company policies related to Internet use. It also highlights the importance of having clear policies in place to guide employees on appropriate Internet use to avoid potential security risks and the negative consequences that can result from misuse.

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The z-score that has 2.5% of the normal distribution below it is approximately 2.06.

To find the z-score that has 2.5% of the normal distribution below it, we need to use the standard normal distribution table (also known as the z-table or normal distribution table). This table shows the area under the standard normal curve to the left of a given z-score.

First, we need to find the area to the left of the desired z-score, which is 2.5%. Then, we need to find the corresponding z-score in the z-table.

Looking at the z-table, we find the row that contains the first digit(s) of the desired z-score, which is 2.5 in this case. Then, we find the column that corresponds to the second decimal place of the desired z-score, which is 0.00 in this case. The intersection of this row and column gives us the area under the standard normal curve to the left of the z-score.

In this case, we find that the area to the left of the z-score is 0.4938. To find the z-score that corresponds to this area, we look in the body of the table and find the closest value to 0.4938, which is 0.01. The corresponding z-score in the row and column headers is 2.06.

Therefore, the z-score that has 2.5% of the normal distribution below it is approximately 2.06.

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The height of the right triangle is 8.66 units.

The side of a right angle triangle can be found using Pythagoras's theorem as follows:

c² = a² + b²

where

Therefore, let's find the base of the bigger triangle.

Therefore, let's find the height using the ratios as follows:

15 / x = x / 5

cross multiply

x² = 75

square root both sides

x = √75

x = 8.66025403784

x = 8.66 units

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Mean of the distribution of sample mean differences (men bpm - women bpm) is -4.3.

The mean of the distribution of sample mean differences (men bpm - women bpm) can be calculated using the formula:

mean difference = mean men bpm - mean women bpm

From the given information, we know that the mean men bpm is 82.8 and the mean women bpm is 87.1. Thus, the mean difference can be calculated as:

mean difference = 82.8 - 87.1
mean difference = -4.3

Therefore, the mean of the distribution of sample mean differences (men bpm - women bpm) is -4.3.

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