## MATH 221 Statistics for Decision Making – DeVry

**1. Question : (TCO 6)** In the standard normal distribution, the standard deviation is always

**2. Question : (TCO 6)** The area under a normal curve with mu = 8 and sigma = 3 is

**3. Question : (TCO 6)** If Larry gets a 70 on a physics test where the mean is 65 and the standard deviation is 5.8, where does he stand in relation to his classmates?

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

**5. Question : (TCO 6) **Let’s assume you have taken 100 samples of size 64 each from a normally distributed population. Calculate the standard deviation of the sample means if the population’s variance is 49.

** 6. Question : (TCO 6)** The area to the left of ‘z’ is 0.9976. What z-score corresponds to this area?

**7. Question : (TCO 6)** Find P(9 < x < 22) when mu = 20 and sigma = 5.

**8. Question : (TCO 7)** What is the critical z-value that corresponds to a confidence level of 86%?

** 9. Question : (TCO 7)** Compute the population mean margin of error for a 90% confidence interval when sigma is 4 and the sample size is 36.

**10. Question : (TCO 7)** A standard IQ test has a mean of 98 and a standard deviation of 16. We want to be 99% certain that we are within 8 IQ points of the true mean. Determine the sample size.

** 11. Question : (TCO 7)** A private medical clinic wants to estimate the true mean annual income of its patients. The clinic needs to be within $500 of the true mean. The clinic estimates that the true population standard deviation is around $2,300. If the confidence level is 95%, find the required sample size in order to meet the desired accuracy.

**12. Question : (TCO 7)** An auditor wants to estimate what proportion of a bank’s commercial loan files are incomplete. The auditor wants to be within 10% 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.

**Explanatory **

**1. Question : (TCO 7) **Interpret a 95% confidence interval of (3.355, 3.445) for the population mean.

**2. Question : (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 $52,500 with a standard deviation of $1,800. 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. Question : (TCO 7)** An auditor wants to estimate what proportion of a bank’s commercial loan files are incomplete. The auditor randomly samples 60 files and finds 12 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.