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1.Listed below are the 35 members of the Metro Toledo Automobile Dealers Association. We would like to estimate the mean revenue from dealer service departments. The members are identified by numbering them 00 through 34.

Picture

We want to select a random sample of five dealers. The random numbers are: 17, 78, 28, 34, 32, 37, 45, 61, 65, 82, 11 and 45. Which dealer ID numbers would be included in the sample? (Enter the numbers as they appear in the spaces below, not their names.)

A sample is to consist of every eighth dealer. The number 1 is selected as the starting point. Which dealer ID numbers are included in the sample? Enter the ID numbers in the order they appear.

2.A population consists of the following five values: 11, 12, 16, 17, and 22.
a.

List all samples of size 3, and compute the mean of each sample. (Round your mean value to 2 decimal places.)
Sample Values Sum Mean
1
2
3
4
5
6
7
8
9
10
b.

Compute the mean of the distribution of sample means and the population mean. (Round your answers to 2 decimal places.)
Sample means
Population mean

3.There are five sales associates at Mid-Motors Ford. The five associates and the number of cars they sold last week are:

Sales Associate Cars Sold
Peter Hankish 8
Connie Stallter 6
Juan Lopez 4
Ted Barnes 10
Peggy Chu 6
a. How many different samples of size 2 are possible without replacement?
Samples of size
b. Compute the mean of each sample.
Cars sold Sample mean
8,6
8,4
8,10
8,6
6,4
6,10
6,6
4,10
4,6
10,6
c.

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

4.In the Department of Education at UR University, student records suggest that the population of students spends an average of 5.10 hours per week playing organized sports. The population’s standard deviation is 2.00 hours per week. Based on a sample of 64 students, Healthy Lifestyles Incorporated (HLI) would like to apply the central limit theorem to make various estimates.
a. Compute the standard error of the sample mean. (Round your answer to 2 decimal places.)
Standard error
b.

What is the chance HLI will find a sample mean between 4.4 and 5.8 hours? (Round z and standard error values to 2 decimal places and final answer to 4 decimal places.)
Chance
c.

Calculate the probability that the sample mean will be between 4.7 and 5.5 hours. (Round z and standard error values to 2 decimal places and final answer to 4 decimal places.)
Probability
d. How strange would it be to obtain a sample mean greater than 7.30 hours?

5.The mean amount purchased by a typical customer at Churchill’s Grocery Store is $21.00 with a standard deviation of $7.00. Assume the distribution of amounts purchased follows the normal distribution. For a sample of 42 customers, answer the following questions.

a.

What is the likelihood the sample mean is at least $22.50? (Round z value to 2 decimal places and final answer to 4 decimal places.)
Probability
b.

What is the likelihood the sample mean is greater than $20.00 but less than $22.50? (Round z value to 2 decimal places and final answer to 4 decimal places.)
Probability
c.

Within what limits will 99 percent of the sample means occur? (Round your answers to 2 decimal places.)
Sample mean and

6.The mean age at which men in the United States marry for the first time follows the normal distribution with a mean of 24.6 years. The standard deviation of the distribution is 2.8 years.

For a random sample of 69 men, what is the likelihood that the age at which they were married for the first time is less than 24.9 years? (Round z value to 2 decimal places. Round your answer to 4 decimal places.)
Probability

7.Crossett Trucking Company claims that the mean weight of its delivery trucks when they are fully loaded is 5,900 pounds and the standard deviation is 155 pounds. Assume that the population follows the normal distribution. Forty trucks are randomly selected and weighed.

Within what limits will 95 percent of the sample means occur? (Round your z-value to 2 decimal places and final answers to 1 decimal place.)
Sample means to

8.Power +, Inc. produces AA batteries used in remote-controlled toy cars. The mean life of these batteries follows the normal probability distribution with a mean of 37 hours. hours and a standard deviation of 5.5 hours. As a part of its quality assurance program, Power +, Inc. tests samples of 9 batteries.

a. What can you say about the shape of the distribution of the sample mean?
Sample mean
b.

What is the standard error of the distribution of the sample mean? (Round your answer to 4 decimal places.)
Standard error
c.

What proportion of the samples will have a mean useful life of more than 38.5 hours? (Round z value to 2 decimal places and final answer to 4 decimal places.)
Probability
d.

What proportion of the sample will have a mean useful life greater than 36.5 hours? (Round z value to 2 decimal places and final answer to 4 decimal places.)
Probability
e.

What proportion of the sample will have a mean useful life between 36.5 and 38.5 hours? (Round z value to 2 decimal places and final answer to 4 decimal places.)
Probability

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