# Probability

Probability

In Excel

1. According to Investment Digest ("Diversification and the Risk/Reward Relationship", Winter 1994, 1-3), the mean of the annual return for common stocks from 1926 to 1992 was 19.4%, and the standard deviation of the annual return was 24.5%. During the same 67-year time span, the mean of the annual return for long-term government bonds was 5.5%, and the standard deviation was 6.0%. The article claims that the distributions of annual returns for both common stocks and long-term government bonds are bell-shaped and approximately symmetric. Assume that these distributions are distributed as normal random variables with the means and standard deviations given previously.

Find the probability that the return for common stocks will be greater than 8%.

Find the probability that the return for common stocks will be greater than 20%.

Hint: There are many ways to attack this problem in the HW. If you would like the normal distribution table so you can draw the pictures (my preferred way of learning) then I suggest you bookmark this site:

http://www.statsoft.com/textbook/sttable.html

Confidence Interval Estimation

2. Compute a 90% confidence interval for the population mean, based on the sample 25, 27, 23, 24, 25, 24, and 59. Change the number from 59 to 24 and recalculate the confidence interval. Using the results, describe the effect of an outlier or extreme value on the confidence interval.

Hypothesis Testing

3. The director of admissions at the University of Maryland, University College is concerned about the high cost of textbooks for the students each semester. A sample of 25 students enrolled in the university indicates that X (bar) = $285.4 and s = $42.20.

a. a. Using the 0.05 level of significance, is there evidence that the population mean is above $300?

b. b. What is your answer in (a) if s = $90 and the 0.10 level of significance is used?

c. c. What is your answer in (a) if X (bar) = $310.10 and s = $40.20?

d. d. Based on the information in part (a), what decision should the director make about the books used for the courses if the goal is to keep the cost below $300?

4. A large hat manufacturer, MICHAELLA HATS, is concerned that the mean weight of their signature Kentucky Derby hat is not greater than 3.5 pounds. It can be assumed that the population standard deviation is .7 pounds based on past experience. A sample of 350 hats is selected and the sample mean is 3.25 pounds. Using a level of significance of .10, is there evidence that the population mean weight of the hats is greater than 3.5 pounds? Fully explain your answer.

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#### Solution Summary

Complete, Neat and Step-by-step Solutions are provided in the attached file.