7.5 Chapter 7 Review Exercises

424

section 7.1

For Exercises 1–5, find and , the mean and standard deviation of the sampling distribution of .

Question 7.178

1. , ,

7.99.1

Question 7.179

2. , ,

Question 7.180

3. , ,

7.99.3

Question 7.181

4. , ,

Question 7.182

5. , ,

7.99.5

For Exercises 6 and 7, if possible find the indicated probability. If it is not possible, explain why not.

Question 7.183

6. Scores on a psychological test are not normally distributed, with and . A sample of size 25 is taken. Find .

Question 7.184

7. Scores on a psychological test are normally distributed, with and . A sample of size 25 is taken. Find .

7.99.7

0.4525

Question 7.185

8. Cocaine and Heart Attacks. The American Medical Association reported: “During the first hour after using cocaine, the user's risk of heart attack increases nearly 24 times. The average age of people in the study who suffered heart attacks soon after using cocaine was only 44. That's about 17 years younger than the average heart attack patient. Of the 38 cocaine users who had heart attacks, 29 had no prior symptoms of heart disease.”9 Assume that the standard deviation of the age of people who suffered heart attacks soon after using cocaine was 10 years and we take a sample of size 38.

  1. Find the 99.5th percentile of the mean age at heart attack after using cocaine.
  2. Find the 0.5th percentile of the mean age at heart attack after using cocaine.
  3. Between which two sample mean ages that are symmetric about the population mean lie 99% of mean ages of all people who suffered heart attacks soon after using cocaine?
  4. By hand, sketch a plot of how this sampling distribution would look

section 7.2

For Exercises 9 and 10, if possible find the indicated probability. If it is not possible, explain why not.

Question 7.186

9. , ,

7.99.9

Not possible since .

Question 7.187

10. , ,

For Exercises 11 and 12, find the indicated value of . If it is not possible, explain why not.

Question 7.188

11. , , the value of smaller than 75% of all values

7.99.11

0.9753

Question 7.189

12. , , the value of smaller than 75% of all values

Question 7.190

13. Women and Depression. According to the National Institute for Mental Health, 12% of women are affected by a depressive disorder each year. Suppose we take samples of 100 women. Answer the following:

  1. Find , where represents the sample proportion of women who are affected by a depressive disorder each year.
  2. Calculate .
  3. Use your answer to (a) to calculate .
  4. Find the 5th and 95th percentiles of the sample proportion.

7.99.13

(a) 0.1093 (b) 0.3907 (c) 0.8907 (d) 0.0665 and 0.1735