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Homework answers / question archive / 1)Listed below are the 35 members of the Metro Toledo Automobile Dealers Association
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. 
(a) 
We want to select a random sample of five dealers. The random numbers are: 65, 4, 65, 27, 45, 25, 66, 8, 18, 28, 69 and 17. Which dealers would be included in the sample? 


(c) 
A sample is to consist of every eighth dealer. The number 0 is selected as the starting point. Which dealers are included in the sample? 


2. The quality control department employs five technicians during the day shift. Listed below is the number of times each technician instructed the production foreman to shut down the manufacturing process last week. 
Technician 
Shutdowns 
Taylor 
4 
Hurley 
3 
Gupta 
5 
Rousche 
5 
Huang 
3 
(a) 
How many samples, without replacement, of size two are possible? 
(b) 
Compute the mean of the sample means and compare it to the population mean. 
Appendix B.6 is a table of random numbers. Hence, each digit from 0 to 9 has the same likelihood of occurrence. A table of random numbers is given below. Assume that these are 5 random samples of five values each. 
(b1) 
Determine the mean of each sample. 
3 
9 
6 
4 
4 
5 
6 
8 
7 
4 
4 
4 
5 
4 
7 
1 
6 
7 
3 
4 
7 
4 
5 
7 
9 
(b2) 
Is this an example of the uniform distribution? 
4.
A normal population has a mean of 58 and a standard deviation of 13. You select a random sample of 25. 
Compute the probability the sample mean is 
(a) 
Greater than 60. 
(b) 
Less than 57. 
(c) 
Between 57 and 60. 0.5642, found by 0.4236 + 0.1406. 
5.
Mattel Corporation produces a remotecontrolled car that requires three AA batteries. The mean life of these batteries in this product is 36 hours. The distribution of the battery lives closely follows the normal probability distribution with a standard deviation of 5.1 hours. As a part of their testing program Sony tests samples of 25 batteries. 
(a) 
What can you say about the shape of the distribution of sample mean? 
(b) 
What is the standard error of the distribution of the sample mean? 
(c) 
What proportion of the samples will have a mean useful life of more than 38 hours? 
(d) 
What proportion of the sample will have a mean useful life greater than 34 hours? 
(e) 
What proportion of the sample will have a mean useful life between 34 and 38 hours? 
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 2.9 years. 
For a random sample of 64 men, what is the likelihood that the age at which they were married for the first time is less than 24.9 years? 
7.
Human Resource Consulting (HRC) is surveying a sample of 76 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 $503 with a standard deviation of $115. 
(a) 
Compute the standard error of the sample mean for HRC 
(b) 
What is the chance HRC finds a sample mean between $477 and $527? 
(c) 
Calculate the likelihood that the sample mean is between $492 and $512. 
(d) 
What is the probability the sample mean is greater that $550? 
8.
Given below are the last four digits of 18 random phone numbers of your local population. 






3,138 
3,898 
4,498 
9,443 
5,319 
9,223 
2,366 
1,001 
3,653 
4,895 
5,819 
3,135 
6,201 
9,585 
5,022 
4,322 
9,856 
4,128 

9.
Crossett Trucking Company claims that the mean weight of its delivery trucks when they are fully loaded is 6,100 pounds and the standard deviation is 160 pounds. Assume that the population follows the normal distribution.Twenty trucks are randomly selected and weighed. 
Within what limits will 99 percent of the sample means occur? 
10.
Suppose your statistics instructor gave six examinations during the semester. You received the following grades (percent correct): 79, 73, 88, 90, 95, and 77. Instead of averaging the six scores, the instructor indicated he would randomly select two grades and compute the final percent correct based on the two percents. 
(a) 
How many different samples , without replacement, of two test grades are possible? 
(c) 
Compute the mean of the sample means and compare it to the population mean. 
11.
In the Department of Education at UR University, student records suggest that the population of students spends an average of 5.60 hours per week playing organized sports. The population's standard deviation is 2.00 hours per week. Based on a sample of 49 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. 
(b) 
What is the chance HLI will find a sample mean between 5 and 6.2 hours? 
(c) 
Calculate the probability that the sample mean will be between 5.4 and 5.8 hours. 
(d) 
How strange would it be to obtain a sample mean greater than 8 hours? 


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