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#### 1) A population consists of the following five values: 12, 12 14, 15, and 20

###### Economics

1) A population consists of the following five values: 12, 12 14, 15, and 20.

1. List all samples of size 3, and compute the mean of each sample.
 Sample Values Sum Mean 1 12,12,14 38 12.66 2 12,12,15 39 13 3 12,12,20 44 14.66 4 14,15,20 49 16.33 5 12,14,15 41 13.66 6 12,14,15 41 13.66 7 12,15,20 47 15.66 8 12,15,20 47 15.66 9 12,14,20 46 15.33 10 12,14,20 46 15.33

1. Compute the mean of the distribution of sample means and the population mean. Compare the two values.
2. Compare the dispersion in the population with that of the sample means.

2) In the law firm Tybo and Associates, there are six partners. Listed below is the number of cases each associate actually tried in court last month.

1. How many different samples of 3 are possible?
2. List all possible samples of size 3, and compute the mean number of cases in each sample.
 Sample Cases sum Mean Ruud, Wu, Saas 3,6,3 12 4 Ruud, Sass, Flores 3,3,3 9 3 Ruud, Flores, Wilhelms 3,3,0 6 2 Ruud, Wilhelms, Schueller 3,0,1 4 1.33 Wu, Flores Ruud 6,3,3 12 4 Wu, Sass, Flores 6,3,3 12 4 Wu, Flores, Wilhelms 6,3,0 9 3 Wu, Wilhelms, Schueller 6,0,1 7 2.33 Sass, Flores, Wilhelms 3,3,0 6 2 Saas, Ruud, Flores 3,3,3 9 3 Saas, Wilhelms, Schueller 3,0,1 4 1.33 Flores, Wilhelms, Schueller 3,0,1 4 1.33 Flores, Wilhelms, Ruud 3,0,3 6 2 Wilhelms,Ruud, Wu 0,3,6 9 3 Wilhelms, Ruud, Saas 0,3,3 6 2 Schueller, Flores, Saas 1,3,3 7 2.33 Schueller, Flores, Wu 1,3,6 10 3.33 Schueller, Flores, Ruud 1,3,3 7 2.33 Wilhelms, Saas, Wu 0,3,6 9 3 Flores, Wilhelms, Saas 3,0,3 6 2 Saas, Flores, Schueller 3,3,1 7 2.33

1. Compare the mean of the distribution of sample means to the population mean.

1. On a chart similar to Chart 8-1, compare the dispersion in the population with that of the sample means.

3) A normal population has a mean of 60 and a standard deviation of 12. You select a random sample of 9. Compute the probability the sample mean is:

1. Greater than 63.

1. Less than 56.

1. Between 56 and 63.

4.) A normal population has a mean of 75 and a standard deviation of 5. You select a sample of 40. Compute the probability the sample mean is:

1. Less than 74.

1. Between 74 and 76.

1. Between 76 and 77.

1. Greater than 77.

5.) According to an IRS study, it takes a mean of 330 minutes for taxpayers to prepare, copy, and electronically file a 1040 tax form. This distribution of times follows the normal distribution and the standard deviation is 80 minutes. A consumer watchdog agency selects a random sample of 40 taxpayers.

1. What is the standard error of the mean in this example?
2. What is the likelihood the sample mean is greater than 320 minutes?

1. What is the likelihood the sample mean is between 320 and 350 minutes?

1. What is the likelihood the sample mean is greater than 350 minutes? .

6.) Recent studies indicate that the typical 50-year-old woman spends \$350 per year for personal-care products. The distribution of the a mounts spent follows a normal distribution with a standard deviation of \$45 per year. We select a random sample of 40 women. The mean amount spent for those sampled is \$335. what is the likelihood of finding a sample mean this large or larger from the specified population? 0.9826

7.) Information from the American Institute of Insurance indicates the mean amount of life insurance per household in the United States is \$110,000. This distribution follows the normal distribution with a standard deviation of \$40,000.

1. If we select a random sample of 50 households, what is the standard error of the mean?
2. What is the expected shape of the distribution of the sample mean?
3. What is the likelihood of selecting a sample with a mean of at least \$112,000?
4. What is the likelihood of selecting a sample with a mean of more than \$100,000?

1. Find the likelihood of selecting a sample with a mean of more than \$100,000 but less than \$112,000.

8.) The mean age at which men in the United States marry for the first time follows the normal distribution with a mean of 24.8 years. The standard deviation of the distribution is 2.5 years. For a random sample of 60 men, what is the likelihood that the age at which they were married for the first time is less than 25.1 years?

9.) Over the past decade the mean number of members of the Information Systems Security Association who have experienced a denial-of-service attack each year is 510 with a standard deviation of 14.28 attacks. Suppose nothing in this environment changes.

1. What is the likelihood this group will suffer an average of more than 600 attacks in the next 10 years?

1. Compute the probability the mean number of attacks over the next 10 years is between 500 and 600.

1. What is the possibility they will experience an average of less than 500 attacks over the next 10 years?

10.) The Oil Price Information Center reports the mean price per gallon of regular gasoline is \$3.79 with a population standard deviation of \$0.18. Assume a random sample of 40 gasoline stations is selected and their mean cost for regular gasoline is computed.

1. What is the standard error of the mean in this experiment?
2. What is the probability that the sample mean is between \$3.77 and \$3.81?

1. What is the probability that the difference between the sample mean and the population mean is less than 0.01?
2. What is the likelihood the sample mean is greater than \$3.87? .

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