# Math 221 week 7 quiz

## 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.

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