Suppose 30% of a population possess a given characteristic. If a random sample of size 1200 is drawn from the population, then the probability that less than 348 possess that characteristic is

Answers

Answer 1

Answer:

The probability that less than 348 possess that characteristic is 0.2148 = 21.48%.

Step-by-step explanation:

I am going to use the binomial approximation to the normal to solve this question.

Binomial probability distribution

Probability of exactly x sucesses on n repeated trials, with p probability.

Can be approximated to a normal distribution, using the expected value and the standard deviation.

The expected value of the binomial distribution is:

[tex]E(X) = np[/tex]

The standard deviation of the binomial distribution is:

[tex]\sqrt{V(X)} = \sqrt{np(1-p)}[/tex]

Normal probability distribution

Problems of normally distributed samples can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

When we are approximating a binomial distribution to a normal one, we have that [tex]\mu = E(X)[/tex], [tex]\sigma = \sqrt{V(X)}[/tex].

In this question, we have that:

[tex]n = 1200, p = 0.3[/tex]

So

[tex]\mu = E(X) = np = 1200*0.3 = 360[/tex]

[tex]\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{1200*0.3*0.7} = 15.8745[/tex]

The probability that less than 348 possess that characteristic is

Using continuity correction, this is P(X < 348 - 0.5) = P(X < 347.5), which is the pvalue of Z when X = 347.5. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{347.5 - 360}{15.8745}[/tex]

[tex]Z = -0.79[/tex]

[tex]Z = -0.79[/tex] has a pvalue of 0.2148.

The probability that less than 348 possess that characteristic is 0.2148 = 21.48%.

Answer 2

The population follows a normal distribution.

The probability that less than 348 possess that characteristic is 0.2248

The given parameters are:

[tex]\mathbf{n = 1200}[/tex]

[tex]\mathbf{p = 30\%}[/tex]

Start by calculating the mean:

[tex]\mathbf{\mu =np}[/tex]

[tex]\mathbf{\mu =1200 \times 30\%}[/tex]

[tex]\mathbf{\mu =360}[/tex]

Calculate the standard deviation

[tex]\mathbf{\sigma = \sqrt{np(1 - p)}}[/tex]

[tex]\mathbf{\sigma = \sqrt{360(1 - 30\%)}}[/tex]

[tex]\mathbf{\sigma = \sqrt{252}}[/tex]

[tex]\mathbf{\sigma = 15.87}[/tex]

Calculate the z-score

[tex]\mathbf{z = \frac{x - \mu}{\sigma}}[/tex]

Where:

x = 348

So, we have:

[tex]\mathbf{z = \frac{348 - 360}{15.87}}[/tex]

[tex]\mathbf{z = -\frac{12}{15.87}}[/tex]

[tex]\mathbf{z = -0.7561}[/tex]

So, the probability is represented as:

[tex]\mathbf{P(x < 348) = P(z < -0.7561)}[/tex]

From the z-table of probabilities, we have:

[tex]\mathbf{P(x < 348) = 0.2248}[/tex]

Hence, the probability that less than 348 possess that characteristic is 0.2248

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Related Questions

WHAT IS 666x666 help me

Answers

Answer:

666 x 666 = 443,556

Answer:

443556

Step-by-step explanation:

666 * 666 = 443556

666

x666

-------

443556

A rectangular prism has a length of 12in, a height of 5in, and a width of 8in. What is its volume, in cubic in?

Answers

Answer: 480 in^3

Step-by-step explanation:

v= l * w*h

v = 12 * 8 * 5

v=  480

ABC is a straight angle.which equation can be used to find the measure of the unknown angle?

Answers

Answer:

Straight angles are all 180 degrees, so it must be an equation that equals 180. I hope that this helps! be saffffeee!

Answer:

140 x 180

Step-by-step explanation:

What is the volume, in cubic in, of a rectangular prism with a height of 6in, a width of 10in, and a length of 2in?

Answers

The answer is 120

do 6 times 10 = 60

then 60 x 2 = 120 cubic in

120 cubic in is the volume of the rectangular prism.

What is volume?

Volume, which is measured in cubic units, is the 3-dimensional space occupied by matter or encircled by a surface. The cubic meter (m³), a derived unit, is the SI unit of volume. Volume is another word for capacity.

The volume of a rectangular prism is given by the formula:

V = lwh,

where l is the length, w is the width, and h is the height.

Plugging in the given values, we get:

V = (2 in) x (10 in) x (6 in)

V = 120 cubic in

Therefore, the volume of the rectangular prism is 120 cubic in.

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What is the value of the 6 In the number 48.061

Answers

Answer:

.06 or six hundredths

Step-by-step explanation:

Answer:

Hundredth place

A lodge rents snowboards for $40/day plus a $20 flat fee for safety gear. Write an equation to represent the relationship between the total cost, c, and number of days renting a snowboard, d.

Answers

Answer:

(40+20)^d=c

Step-by-step explanation:

Answer:= let me double check yall

Step-by-step explanation:40+20+c+d

Triangle A B C is shown. Angle A B C is 95 degrees and angle B C A is 45 degrees. The length of A B is c and the length of B C is 3.0 centimeters. Law of sines: StartFraction sine (uppercase A) Over a EndFraction = StartFraction sine (uppercase B) Over b EndFraction = StartFraction sine (uppercase C) Over c EndFraction Which represents the value of c? C = StartFraction (3) sine (40 degrees) Over sine (45 degrees) EndFraction c = StartFraction (3) sine (45 degrees) Over sine (40 degrees) EndFraction c = StartFraction sine (40 degrees) Over (3) sine (45 degrees) EndFraction c = StartFraction sine (45 degrees) Over (3) sine (40 degrees)

Answers

Answer:

(B)c = StartFraction (3) sine (45 degrees) Over sine (40 degrees) EndFraction

[tex]c=\dfrac{3 * \sin 45}{sin 40}[/tex]

Step-by-step explanation:

In Triangle ABC is shown.

[tex]\angle A B C=[/tex] 95 degrees

[tex]\angle B C A =[/tex] 45 degrees.

|AB|=c

|BC|=3.0 cm

[tex]\angle A+\angle B+\angle C=180^\circ\\\angle A+95+45=180\\\angle A=180-140=40^\circ[/tex]

Using the Law of Sines

[tex]\dfrac{a}{\sin A}=\dfrac{b}{\sin B}=\dfrac{c}{\sin C}[/tex]

[tex]\dfrac{3}{\sin 40}=\dfrac{c}{\sin 45}\\\\$Cross multiply\\c*\sin 40 =3 * \sin 45\\\\c=\dfrac{3 * \sin 45}{sin 40}[/tex]

The correct option is B.

Answer:

B

Step-by-step explanation:

Ellen mixed \dfrac1{4}\text{ kg} 4 1 ​ kgstart fraction, 1, divided by, 4, end fraction, start text, space, k, g, end text of flour with \dfrac{2}{9}\text{ kg} 9 2 ​ kgstart fraction, 2, divided by, 9, end fraction, start text, space, k, g, end text of sugar.

Answers

Question:

Ellen mixed ¼ kg of flour with ²/9 kg of sugar.

Answer:

See Explanation

Step-by-step explanation:

The question is incomplete. However, question that are likely to be asked are.

- What's the weight of the total mixture in grams

- What percentage of the mixture is sugar

To solve (1);

We simply add both weights together

But first, the units must be converted to grams.

1kg = 1000 grams

So,

¼kg = ¼ * 1000 g

¼kg = 250 g

²/9kg = ²/9 * 1000

²/9kg = 2000/9

²/9kg = 222.2 g

Add these results

Total = 250g + 222.2g

Total = 472 g

The result can be written in different ways

1. 472 grams

2. About 500 grams

If converted back to kg

472 grams = 472/1000 kg

472 grams = 0.472 kg.

So, the result can also be written as

3. 0.472 kg

4. About 0.5kg (½kg)

To solve (2)

What percentage of the mixture is sugar

To do this, we simply divide the size of sugar by the total size of the mixture.

From (1) above

Sugar = 250g

Total = 472g

Percentage of sugar = 250/472

Percentage of sugar = 0.5297

Percentage of sugar = 0.5297 * 100%

Percentage of sugar = 52.97%

Answer:

1/2

Step-by-step explanation:

I did it and it was write right hope it helps

80 POINTS! Help with this question please!!!! 80 POINTS!

Answers

Answer:

C. Translation 5 units left and 2 units down

Step-by-step explanation:

Let's take a look at A', which is (0, 0). This is the result of A, which is (5, 2) being transformed somehow. Notice that the x-coordinate moved 5 units to the left (from 5 to 0, which means we subtract 5 from 5). And, notice that the y-coordinate moved 2 units down (from 2 to 0, so we subtract 2 from 2).

Look to see if this works for the other two points:

B(6, 1): if we subtract 5 from the x-coordinate 6, we get 6 - 5 = 1, which matches the x-coordinate of the image B'. If we subtract 2 from the y-coordinate of B, which is 1, we get 1 - 2 = -1, which also matches the y-coordinate of B'. So, this works.

C(4, 5): if we subtract 5 from the x-coordinate 4, we get 4 - 5 = -1, which matches the x-coordinate of the image C'. If we subtract 2 from the y-coordinate of C, which is 5, we get 5 - 2 = 3, which also matches the y-coordinate of C'. So, this again works.

Therefore, we know that the transformation is a translation 5 units left and 2 units down, or C.

A picture will be shown below of a graph with the points in the table.

We only need to use (5, 2) and (0, 0) to solve this problem.

We take both points and see what it took for the old point to get to where the new point is (Shown in picture below).

Therefore, the answer is [ C. Translation 5 units left and 2 units down ]

Best of Luck!

The perimeter of quadrilateral ABCD is 640. The perimeter of quadrilateral LMNO is 144. What is LM

Answers

Answer:

LM = 36

Step-by-step explanation:

A quadrilateral is a shape with 4sides. There are different type of quadrilateral such as square, rectangle, trapezium, parallelogram, kite and rhombus.

Perimeter of a quadrilateral is the addition of all 4 sides.

Since the shape is not specified neither is there a diagram, let's assume the quadrilateral is a square.

See attachment for diagram used in solving the question.

Perimeter of square = length+ length+ length+ length

= 4× length

Perimeter of quadrilateral ABCD:

640 = 4×length

Length = 640/4

Length = 160

Perimeter of quadrilateral LMNO:

144 = addition of all 4 lengths

144 = LM + MN + NO +OL

Since we are considering a square all the sides are equal.

LM = MN = NO = OL

144 = 4×LM

LM = 144/4

LM = 36

please please help i will mark brainlist

Answers

Answer:

Answer is option a) 4/5

Here value of opposite side is 40

And the value of hypotenuse is 50

Step-by-step explanation:

[tex] \sin(C) = \frac{opposite \: side \: }{hypotenuse} \\ = \frac{40}{50} \\ = \frac{4}{5} [/tex]

HAVE A NICE DAY!

THANKS FOR GIVING ME THE OPPORTUNITY TO ANSWER YOUR QUESTION.

Denzel wants to walk to the store from his house but he is not sure how far away it is. Find the distance between his house

(-8, -9) and the store (-4, -10). Each unit is equal to one mile. Round your answer to the nearest mile.



22 miles


4 miles


31 miles


17 miles

Answers

Answer:

4 miles

Step-by-step explanation:

Suppose we have two points:

[tex]A = (x_{1}, y_{1})[/tex]

[tex]B = (x_{2}, y_{2})[/tex]

The distance between these points is:

[tex]D = \sqrt{(x_{2} - x_{1})^{2} + (y_{2} - y_{1})^{2}}[/tex]

In this question:

Points (-8, -9) and (-4, -10).

So the distance is:

[tex]D = \sqrt{(-8 - (-4))^{2} + (-9 - (-10))^{2}} = \sqrt{17} = 4.12[/tex]

The distance is 4.12 miles.

Rounding to the nearest mile, 4 miles.

Find the slope: (-1,5) and (2,-3)

Answers

Answer:

-2/3

Step-by-step explanation:

Answer:

(-3-5)/(2-(-1))=-8/3

Step-by-step explanation:

help me please i am confused on what to do

Answers

It would be 32 minutes
20 /150= then multiply by 240

What is the 14th term in the sequence 6n + 1

Answers

Answer:

85

Step-by-step explanation:

6(14)+1=

84+1=

85

Hope this helps! please mark brainliest :)

PLEASE HELP I'VE ASKED THIS 2 TIMES NOW PLEASE HELP

Can adjacent angles be complementary?

Give a brief explanation as to why or why not.

Answers

Answer:

Two adjacent angles can be complementary

Step-by-step explanation:

if they add up to 90°. For example, a diagonal of a square will split the right angle into two equal angles; 45°+45°. In a right triangle, the altitude from a right angled vertex will split the right angle into two adjacent angles; 30°+60°, 40°+50°, etc.

Using the distributive law, work out
the solution for the following:
87 x 63 + 87 x 37

Answers

Answer:

the answer is 8700

Step-by-step explanation:

(87 x 63) + (87 x 37)= 8700

hope this helps :-)

A missing data value from a set of data has a z-score of –2.1. Fred already calculated the mean and standard deviation to be Mu = 43 and Sigma = 2. What was the missing data value? Round the answer to the nearest whole number. 39 41 45 47

Answers

Answer:

39

Step-by-step explanation:

i just did it on usa test prep

Using the normal distribution, it is found that the missing data value was of 39.

Normal Probability Distribution

In a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

It measures how many standard deviations the measure is from the mean. After finding the z-score, we look at the z-score table and find the p-value associated with this z-score, which is the percentile of X.

In this problem, we have that:

[tex]\mu = 43, \sigma = 2, Z = -2.1[/tex]

The missing data value is X, hence:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]-2.1 = \frac{X - 43}{2}[/tex]

[tex]X - 43 = -4.2[/tex]

[tex]X = 38.8[/tex]

Rounding up, the missing data value was of 39.

More can be learned about the normal distribution at https://brainly.com/question/14424710

How do I use D = rt to find the distance (D) where r = 6 and t =9?

Answers

Answer:

The answer will be 54

Step-by-step explanation:

D = r x t

R equals to 6 and t equals to 9

So, substitute r with 6 and t with 9 which will give you distance = 6 x 9 = 54

what is the slope of the equation 3y=9x-6?

Answers

Answer:

It's 3

Step-by-step explanation:

Just divide the entire equation by 3 to isolate the y variable on the left side.

y = mx + b (m is the slope)

and in this equation, after you divide by 3, the value of m is 3.

2) Shawn's cat is currently stuck in a tree. Shawn has a ladder that is 15 feet long and he places the ladder 10 feet from the base of the tree. At what angle of depression is Shawn's cat looking at him?

Answers

Answer:

48.19°

Step-by-step explanation:

Check the attachment for the diagram.

The set up is a right angled triangle

Using the SOH, CAH, TOA trigonometry ratio to get the angle of depression theta.

The length of the ladder will be the hypotenuse of the triangle.

If he places the ladder 10 feet from the base of the tree, the adjacent of the triangle will be the base of the triangle.

Given Hypotenuse = 15feet

Adjacently = 10feet

According to CAH;

cos(theta) = Adjacent/Hypotenuse

cos(theta) = 10/15

cos(theta) = 2/3

theta = arccos(2/3)

theta = 48.19°

Shawn cat is looking at him at an angle of depression of 48.19°

I NEED HELP NOWwwwwwww

Answers

Answer:

523 cm^3

Step-by-step explanation:

The volume of a sphere  is

V = 4/3 pi r^3

V = 4/3 (3.14) (5)^3

V = 523.33333

Rounding to the nearest whole number

V = 523

PLEASE HELP ME WITH PRE CAL!!

A drone is flying over a college campus. The drone spots the cafeteria on the west end of campus at a 27 ° angle of depression and the sports complex on the east end of campus at a 34° angle of depression. If the cafeteria and sports complex are separated by a straight road 2.3 mi long, how high is the drone?

Answers

Answer:

0.67 mi

Step-by-step explanation:

The diagram illustrating the question is shown in the attach photo.

In triangle DCA,

Opposite = H

Adjacent = b

Angel θ = 27°

Tan θ = Opp /Adj

Tan 27° = H/b

Cross multiply

H = b x Tan 27°... (1)

From triangle DSA,

The diagram illustrating the question is shown in attach photo.

In triangle DCA,

Opposite = H

Adjacent = 2.3 – b

Angel θ = 34°

Tan θ = Opp /Adj

Tan 34° = H/ 2.3 – b

Cross multiply

H = Tan 34° (2.3 – b) .. (2)

Equating equation (1) and (2)

b x Tan 27° = Tan 34° (2.3 – b)

0.5095b = 0.6745(2.3 – b)

0.5095b = 1.55135 – 0.6745b

Collect like terms

0.5095b + 0.6745b = 1.55135

1.184b = 1.55135

Divide both side by 1.184

b = 1.55135/1.184

b = 1.31 mi

Substitute the value of b into any of the equation to obtain the height (H). In this case we shall use equation 1.

H = b x Tan 27°

H = 1.31 x Tan 27°

H = 0.67 mi

Therefore, the height of the drone is 0.67 mi

The height of the drone is 0.67 mi

The calculation is as follows:

In triangle DCA,

Opposite = H

Adjacent = b

Angel θ = 27°

Tan θ = [tex]Opp \div Adj[/tex]

Tan 27° =[tex]H\div b[/tex]

Now we have to do the cross multiply

[tex]H = b \times Tan 27^{\circ}... (1)[/tex]

Now

From triangle DSA,

In triangle DCA,

Opposite = H

Adjacent = 2.3 – b

Angel θ = 34°

Tan θ = [tex]Opp \div Adj[/tex]

Tan 34° = [tex]H\div 2.3 - b[/tex]

Now we have to do the cross multiply

H = Tan 34° (2.3 – b) .. (2)

Now

Equating equation (1) and (2)

[tex]b \times Tan 27^{\circ} = Tan 34^{\circ} (2.3 - b)[/tex]

0.5095b = 0.6745(2.3 – b)

0.5095b = 1.55135 – 0.6745b

Now

0.5095b + 0.6745b = 1.55135

1.184b = 1.55135

b = 1.31 mi

Now

[tex]H = b \times Tan 27^{\circ}\\\\H = 1.31 \times Tan 27^{\circ}[/tex]

H = 0.67 mi

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Charlotte have 36 apple,Dylan have 1 apple and Kevin have 56 apple how many apples are left?

Answers

Answer:

93 apples?

Step-by-step explanation:

36 + 1 + 56 = 93 apples?


a. How many groups of 6 erasers can be formed from the 18 erasers? Explain.
b. In how many ways can 3 aliens be selected? Explain.
c. In how many ways can 3 aliens and 3 flying saucers be selected? Explain.
d. What is the probability that 3 aliens and 3 flying saucers will be selected? Explain.
in​

Answers

Answer:

Step-by-step explanation:

Answer:

1.3  groups beucae 18/6=3.

b.???

c.what

d. ru serious

Step-by-step explanation:

What were the causes of the American Revolution? *

Answers

Answer:

The Founding of the Colonies.

French and Indian War.

Taxes, Laws, and More Taxes.

Protests in Boston.

Intolerable Acts.

Boston Blockade.

Growing Unity Among the Colonies.

First Continental Congress.

Step-by-step explanation:

How do I solve this problem? I need to find the volume of this composite figure.

Answers

Step-by-step explanation:

V = (12*4*5) + (2*3*5) + (5*3*5) + (12*4*5)

V = 240 + 30 + 75 + 240

V = 585 cm^3

Please help asap! Will give brainliest! Please answer correctly! No guessing. Check all that apply.

Answers

Answer:F

Step-by-step explanation:

Answer:

i honestly think that its A, C, D, F.

Step-by-step explanation:

for the A i think that you need to write down the facts so you dont forget and you remember when someone asks you a question.

For C you should gather your resources so you can do the experiment again if your not satisfied with the first result.

For D you should draw a diagram so you can keep track of your information that you used to get the final solution.

For F, you should always make sure that you didn't mess up and that you can redo it to double check.

I don’t know how to do this

Answers

Answer:

See attachment

Step-by-step explanation:

A teacup has a radius of 5 centimeters. What is the teacup's diameter? Help please.

Answers

Answer:10

Step-by-step explanation:

Radius is half the diameter

Answer:

10 cm

Step-by-step explanation:

the radius is half the diameter so 5x2=10cm

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