In the library on a university campus, there is a sign in the elevator that indicates a limit of 16 persons. Furthermore, there is a weight limit of 2500 lb. Assume that the average weight of students, faculty, and staff on campus is 151 lb, that the standard deviation is 25 lb, and that the distribution of weights of individuals on campus is approximately normal. If a random sample of 16 persons from the campus is to be taken:

a. What is the expected value of the sample mean of their weights?
b. What is the standard deviation of the sampling distribution of the sample mean weight?
c. What average weights for a sample of 16 people will result in the total weight exceeding the weight limit of 2500 lb?
d. What is the chance that a random sample of 16 persons on the elevator will exceed the weight limit?

Answers

Answer 1

Answer:

Explained below.

Step-by-step explanation:

According to the Central Limit Theorem if an unknown population is selected with mean μ and standard deviation σ and appropriately huge random samples (n > 30) are selected from this population with replacement, then the distribution of the sample means will be approximately normally.  

Then, the mean of the sample means is given by,

[tex]\mu_{\bar x}=\mu[/tex]

And the standard deviation of the sample means is given by,

[tex]\sigma_{\bar x}=\frac{\sigma}{\sqrt{n}}[/tex]

a

The expected value of the sample mean of their weights is same as the population mean, μ = 1515 lbs.

b

The standard deviation of the sampling distribution of the sample mean weight is:

[tex]\sigma_{\bar x}=\frac{\sigma}{\sqrt{n}}=\frac{25}{\sqrt{16}}=6.25[/tex]

c.

The average weights for a sample of 16 people will result in the total weight exceeding the weight limit of 2500 lbs. is:

[tex]\text{Average Weight}=\frac{2500}{16}=156.25[/tex]

d

Compute the probability that a random sample of 16 persons on the elevator will exceed the weight limit as follows:

[tex]P(\bar X > 156.25)=P(\frac{\bar X-\mu_{\bar x}}{\sigma_{\bar x}}>\frac{156.25-151}{6.25})\\\\=P(Z>0.84)\\\\=1-P(Z<0.84)\\\\=1-0.79955\\\\=0.20045\\\\\approx 0.20[/tex]


Related Questions

30% of the cars in a parking lot are green. If there 21 green cars, how many cars are parked in the parking lot?

Answers

Answer:

70 cars

Step-by-step explanation:

Let x cars are parked in the parking lot.

[tex]30\% \: of \: x = 21 \\ \\ \frac{30}{100} \times x = 21 \\ \\ x = 21 \times \frac{100}{30} \\ \\ x = \frac{2100}{30} \\ \\ x = 70 \: [/tex]

70 cars are parked in the parking lot.

find the inverse of the function y equals x squared minus 12 ​

Answers

Answer:

Step-by-step explanation:

y=x^2-12

The inverse is

√x+12, -√x+12

please answer if you can? (This is my math from 8th grade)

Answers

Answer:

40!

Step-by-step explanation:

3x+20+40=180

3x+60=180

3x=120

x=40

Answer:

b=40

Step-by-step explanation:

A new basketball 20% off if it’s original price and is now selling for $36 what is the original price of the basketball before
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Answers

The answer is 180$ hope this helps

A poll commissioned by Friends of the Earth and conducted by the Mellman Group found that 72% of American voters are in favor a carbon tax. Suppose that six voters in the United States are randomly sampled and asked whether they favor a carbon tax. Determine the probability that the number answering in the affirmative is a. Exactly four. b. At least two

Answers

Answer:

a

  [tex]P(X = 4) = 0.31599[/tex]

b

 [tex]P(X  \ge 2) = 0.9921  [/tex]

Step-by-step explanation:

From the question we are told that

    The proportion in favor of carbon tax is  [tex]p = 0.72[/tex]

    The sample size is  n  = 6

Generally the distribution of poll  follows a binomial distribution  

i.e  

         [tex]X  \~ \ \ \  B(n , p)[/tex]

and the probability distribution function for binomial  distribution is  

      [tex]P(X = x) =  ^{n}C_x *  p^x *  (1- p)^{n-x}[/tex]

Here C stands for combination hence we are going to be making use of the combination function in our calculators      

   Generally the probability that the number answering in the affirmative is  4 is mathematically represented as

       [tex]P(X = 4) =  ^{6}C_4 *  (0.72)^4 *  (1- 0.72)^{6-4}[/tex]

=>     [tex]P(X = 4) = 0.31599[/tex]

   Generally the probability that the number answering in the affirmative is At least two is mathematically represented as

     [tex]P(X  \ge 2) =  1 -  P( X <  2 ) [/tex]

     [tex]P(X  \ge 2) = 1- [ P(X =  0 ) + P( X = 1)] [/tex]

=>  [tex]P(X  \ge 2) = 1- [ [ 1 *  1 * 0.00048 ]+ [ 6 * 0.72 * 0.00172] [/tex]

=>    [tex]P(X  \ge 2) = 1- [ 0.00791 ] [/tex]

=>    [tex]P(X  \ge 2) = 0.9921  [/tex]

Given f(x) = 2x2 + 4x - 3 and g(x) = 5x – 2, find f(x) · g(x).
Must show all work to receive credit! Show your work in the box below.

Answers

Answer:

i don't have and idea

Step-by-step explanation:

Which product matches the shading on the grids? ​

Answers

Answer:

I believe it is D. not sure tho

A bag of marbles has 5 blue marbles, 3 red marbles, and 6 yellow marbles. A marble is drawn from the bag at random . How many possible possible outcomes are there?

° 3
° 5
° 6
° 14
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Answers

The anser is 14 I guess because there are 14 marbles in total giving you 14 outcomes

Jordan's net income for the year ended December 31, Year 2 was $200,000.

Answers

I need more information to know what you are asking for an answer

Answer:

good for her / him but uh whats the question

Aarti posted a comment on her blog. Each day the number of responses to her comment was 125% of the number she
received on the previous day. If there were 64 responses the first day, how many were there on the fourth day?
O 100
112
оооо
125
132
Mark this and return
Save and Exit
Next
Submit

Answers

Answer:

125

Step-by-step explanation:

Answer:

125

Step-by-step explanation:

1+6 pls help me nowwwwwww

Answers

Answer:

7

Step-by-step explanation:

Your answer would be 7

Given the point and slope write the equation of the line (6, -6); slope = 5/6

Answers

Answer:

y=5/6x-11

Step-by-step explanation:

Slope intercept form: y=mx+b

With slope: y=5/6x+b

Replace x with 6 and y with -6

[To figure out which one is x or y remember (x,y) so if you compare (6,-6) then you will find that 6 is x and -6 is y]

-6=5/6(6)+b

Simplify:

-6=5+b

Subtract 5 on both sides:

-11=b or b=-11

Answer:y=5/6x-11 (Replace the b in y=5/6x+b with -11 since -11 is equal to b)

Hope this helps!

There are 4 trucks for every 5 cars in a parking lot. If there are 80 cars, how many trucks are in the parking lot?

Answers

Answer:

There are 64 trucks!

Step-by-step explanation:

Divide. Express your answer in simplest form.
8/9 ÷ 8

○7 1/9
○1/9
○8/72
○9​

Answers

Answer:

1/9

Step-by-step explanation:

8/9 ÷ 8/1

8/9 x 1/8 = 8/72

The GCF for 8 and 72 is 8

[tex]\frac{8}{72}[/tex]÷[tex]\frac{8}{8}[/tex]=[tex]\frac{1}{9}[/tex]

Answer: 1/9

see below for work ⤵

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Answers

Answer:

y = ⅓(x - 1425)

Step-by-step explanation:

Given

Budget = x

Mortgage = 1425

Required

Determine the amount spent on recreational activities.

First, we need to get the balance after she pays her mortgage.

Balance = Budget - Mortgage

Balance = x - 1425

From the question, we understand that she spends ⅓ of the balance on recreational activities.

Represent this with y.

y is calculated as thus:

y = ⅓ of Balance

y = ⅓ * (x - 1425)

y = ⅓(x - 1425)

Hence, the above equation y = ⅓(x - 1425) can be used to calculate the amount spent on recreational activities

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Answers

Y= 8x-7 must be the answer

The other equation could be y = 8x - 7

How to determine the other equation?

The first equation is given as:

y = 8x + 7

For the system of equation to have no solution, then the equations in the system would have different constant values.

Take for instance:

y = 8x + b

Where:

b is a constant not equal to 7

From the options, we have:

y = 8x - 7

Notice that -7 and 7 are not the same

Hence, the other equation could be y = 8x - 7

Read more about system of equations at:

https://brainly.com/question/13729904

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Answers

Answer:

3,400

Step-by-step explanation:

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Answer:

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Step-by-step explanation:

A snack-size bag of carrots has a mean weight of 1.75
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Answers

Answer:

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They deserve brainliest

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Answers

Answer:

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Step-by-step explanation:

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Answers

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Answers

Answer:

Jeremy has gotten more than half of the test's questions correctly.

Step-by-step explanation:

To get half of the questions correctly, Jeremy needed at least 40, and Jeremy got more than 40, meaning he got more than half.

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Please show the steps....

Answers

Answer:

4,800

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Answer:

probably

Step-by-step explanation:

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Answers

Answer:

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Step-by-step explanation:

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I hope this helped! <3

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Answers

Answer:

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Step-by-step explanation:

A company has Liabilities of $23,500 and Stockholders' Equity of $56,500. How much
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Answers

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Answers

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Step-by-step explanation:

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Answers

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Step-by-step explanation:

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Answers

Answer:

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Step-by-step explanation:

i hope i read it right

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Step-by-step explanation:

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the price of a video game was reduced by $60 to 45. By what percentage was the price of the video game reduced?

Answers

Answer:

25% reduced

Step-by-step explanation:

45/60= .75

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