# Statistics problems: Analysis method, probability, time intervals

The following information is for Questions 2.

It is an open secret that airlines overbook flights, but I have just learned recently that bookstores underbook (I might have invented this new term.) textbooks..........

To make a long story short, our UMUC designated virtual bookstore, MBS Direct, routinely, as a matter of business practice, orders less textbooks than the amount requested by UMUC's Registrar's Office. That is what I have figured out.......

MBS Direct believes that only 85% of our registered students will stay registered in a class long enough to purchase the required textbook. According to the Registrar's Office, we have 300 students enrolled in UMUC 200 this fall of 2010.

2. Is there an approximate method to carry out the above analysis? Is so, how would you do it?

3. In this recession, a jewelry store owner named Iwana Makemoney would like to make more money. A promising enterprise is to mass-produce garnet wedding rings for brides. Based on his diligent research, he has found out that women's ring size normally distributed with a mean of 6.0, and a standard deviation of 1.0. He is going to order 5000 garnet wedding rings from his reliable Siberian source. They will manufacture ring size from 4.0, 4.5, 5.0, 5.5, 6.0, 6.5, 7.0, 7.5, 8.0, 8.5, 9.0, and 9.5. How many wedding rings should he order for each of the ring size should he order 5000 rings altogether? (Note: It is natural to assume that if your ring size falls between two of the above standard manufacturing size, you will take the bigger of the two.)

4. We have 7 boys and 3 girls in our BSA Venture Crew 829. A trip is planned for the Via Ferrata at the Nelson Rocks Preserve in West Virginia this fall. Unfortunately, we can only bring 5 youths in this trip. This team of 5 has to be picked randomly from the crew of 7 boys and 3 girls.

a. What is the probability that all 3 girls are picked in this team of 5?

b. What is the probability that none of the girls are picked in this team of 5?

c. What is the probability that 2 of the girls are picked in this team of 5?

5. A soda company want to stimulate sales in this economic climate by giving customers a chance to win a small prize for ever bottle of soda they buy. There is a 15% chance that a customer will find a picture of a cherry at the bottom of the cap upon opening up a bottle of soda. The customer can then redeem that bottle cap with a picture of a cherry for a small prize. Now, if I buy a 6-pack of soda, what is the probability that I will win something, i.e., at least win a single small prize?

6. A business manager in our unit has decided that dress code is necessary for unit coherence. Unit staff are required to wear either blue shirts or red shirts. We have 9 men and 7 women in our unit. On a particular day, 5 men wore blue shirts and 4 other wore red shirts, whereas 4 women wore blue shirts and 3 others wore red shirt. Apply the Addition Rule to determine the probability of finding men or blue shirts in our unit.

7. According to a study by PseudoScientific Consulting, the time interval between Atlantic hurricane of category 4 has a mean of 456 days and a standard deviation of 123 days. Suppose that you observe a sample of five (5) time intervals between successive category 4 hurricanes.

a. On average, what would you expect to be the mean of the five (5) time intervals?

b. How much variation would you expect from your answer in part (a)? (Hint: Think along the line of the Empirical 68-95-99.7 Rule.)

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Problem 2

There seems to be some ambiguity in the problem; however, I believe that I get the gist of what is happening. The bookstore believes that 85% of registered students will stay registered. If p represents the true proportion of students that will stay registered, then we wish to test the hypothesis:

H0: p = .85 versus the alternative:

HA: p > .85

In the case of HA, the bookstore will have to order more books and some students may potentially not have their materials in time for the start of class.

Let X be a random variable that represents the number of students out of 300 that remain registered for the class this fall. Then p-hat = X/300 approximates (i.e., estimates) the true population proportion p. The standard deviation of p-hat ...

#### Solution Summary

An analysis method, probability and time intervals are examined.