A population consists of the following five values: 1, 1, 3, 5, 6

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1. A population consists of the following five values: 1, 1, 3, 5, 6.

 

(a)

List all samples of size 3, and compute the mean of each sample. (Round sample means to 2 decimal places.)

 

Sample

Values

Sum

Mean

1

1,1,3

5

1.67

2

1,1,5

7

2.33

3

1,1,6

8

2.67

4

1,3,5

9

3.00

5

1,3,6

10

3.33

6

1,5,6

12

4.00

7

1,3,5

9

3.00

8

1,3,6

10

3.33

9

1,5,6

12

4.00

10

3,5,6

14

4.67

 

(c)

Compute the mean of the distribution of sample means and the population mean.(Round your answers to 1 decimal place.)

 

 
  

 

2. A normal population has a mean of 68 and a standard deviation of 6. You select a sample of 52.

 

Compute the probability the sample mean is (Round z values to 2 decimal places andfinal answers to 4 decimal places):

 

(a)

Less than 67.

(b)

Between 67 and 69.

 (c)

Between 69 and 70.

 (d)

Greater than 70.

 

3.

CRA CDs Inc. wants the mean lengths of the "cuts" on a CD to be 128 seconds (2 minutes and 8 seconds). This will allow the disk jockeys to have plenty of time for commercials within each 10-minute segment. Assume the distribution of the length of the cuts follows the normal distribution with a population standard deviation of 6 seconds. Suppose we select a sample of 21 cuts from various CDs sold by CRA CDs Inc.

 

(a)

What can we say about the shape of the distribution of the sample mean?

 

(b)

What is the standard error of the mean? (Round your answer to 2 decimal places.)

 

(c)

What percent of the sample means will be greater than 130 seconds? (Round your answer to 2 decimal places. Omit the "%" sign in your response.)

 

(e)

What percent of the sample means will be greater than 123 but less than 130 seconds? (Round your answer to 2 decimal places. Omit the "%" sign in your response.)

 

4. Human Resource Consulting (HRC) is surveying a sample of 68 firms in order to study health care costs for a client. One of the items being tracked is the annual deductible that employees must pay. The state Bureau of Labor reports the mean of this distribution is $499 with a standard deviation of $80.

 

(a)

Compute the standard error of the sample mean for HRC. (Round your answer to 2 decimal places.)

 

(b)

What is the chance HRC finds a sample mean between $477 and $527? (Round z value to 2 decimal places and final answer to 4 decimal places.)

 

(c)

Calculate the likelihood that the sample mean is between $492 and $512. (Round z value to 2 decimal places and final answer to 4 decimal places.)

 

(d)

What is the probability the sample mean is greater than $550? (Round z value to 2 decimal places and final answer to 4 decimal places.)

    • 9 years ago
    A population consists of the following five values: 1, 1, 3, 5, 6
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