# Statistics Problem Set and the Standard Normal Distribution

1. (TCO 6) In the standard normal distribution, the variance is always

0

1

2

none of these

2. (TCO 6) The area under the standard normal curve is

0

1

2

none of these

3. (TCO 6) If John gets an 80 on a physics test where the mean is 85 and the standard deviation is 3, where does he stand in relation to his classmates?

He is in the top 5%.

He is in the top 10%.

He is in the bottom 5%.

He is the bottom 1%.

4. (TCO 6) In a normal distribution with mu = 25 and sigma = 6, what number corresponds to z = 3?

40

43

46

none of these

5. (TCO 6) Let's assume you have taken 100 samples of size 49 each from a normally distributed population. Calculate the standard deviation of the sample means if the population's variance is 16.

0.571

0.429

0.327

0.107

6. (TCO 6) The area to the left of 'z' is 0.9192. What z-score corresponds to this area?

1.49

-1.49

1.40

none of these

7. (TCO 6) Find P(9 < x < 15) when mu = 12 and sigma = 2.

0.9332

0.0668

0.8664

0.1336

8. (TCO 7) What is the critical z-value that corresponds to a confidence level of 92%?

approximately 1.48

approximately 1.55

approximately 1.75

none of these

9. (TCO 7) Compute the population mean margin of error for a 99% confidence interval when sigma is 4 and the sample size is 36.

+/- 1.3066...

+/- 1.0966...

+/- 1.7166...

none of these

10. (TCO 7) A standard IQ test has a mean of 98 and a standard deviation of 16. We want to be 90% certain that we are within 8 IQ points of the true mean. Determine the sample size.

27

11

10

none of these

11. (TCO 7) A private medical clinic wants to estimate the true mean annual income of its patients. The clinic needs to be within $200 of the true mean. The clinic estimates that the true population standard deviation is around $1,300. If the confidence level is 95%, find the required sample size in order to meet the desired accuracy.

205

163

200

150

12. (TCO 7) An auditor wants to estimate what proportion of a bank's commercial loan files are incomplete. The auditor wants to be within 7% of the true proportion when using a 95% confidence level. How many files must the auditor sample? No estimate of the proportion is available, so use 0.5 for the population proportion.

196

150

200

180

1. (TCO 7) Interpret a 90% confidence interval of (4.355, 4.445) for a population mean.

2. (TCO 7) A nursing school wants to estimate the true mean annual income of its alumni. It randomly samples 200 of its alumni. The mean annual income was $55,200 with a standard deviation of $1,500. Find a 95% confidence interval for the true mean annual income of the nursing school alumni. Write a statement about the confidence level and the interval you find.

3. (TCO 7) An auditor wants to estimate what proportion of a bank's commercial loan files are incomplete. The auditor randomly samples 100 files and finds 9 are incomplete. Using a 95% confidence interval, estimate the true proportion of incomplete files for ALL the bank's commercial loans. Write a statement about the confidence level and the interval you find.

#### Solution Summary

The solution provides answers and required calculations for the multiple statistical problems.