Exam 2   Math 308   Friday October 8, 2010

Name___________________________________

1.	(15 pts) In 2001, Masterfoods, the manufacturer of M&M’s decided to add another color to the standard color lineup of brown, yellow, red, orange, blue and green. To decide which color to add, they surveyed kids in nearly every country of the world and asked to vote among purple, pink and teal. In USA, 45% of those who voted said purple, 35% said teal, and only 20% said pink. 
a.	What is the probability that a USA respondent prefers pink of teal?
b.	If we ask 5 randomly chosen kids in the USA, what is the probability that they all prefer purple?
c.	If we ask 5 randomly chosen kids in the USA, what is the probability that at least one of kid does not prefer purple?
d.	If we ask 5 randomly chosen kids in the USA, what is the probability that the first or the second prefer pink?

2.	(15 pts) A fast food restaurant just leased a new freezer for five years. The service contract for the freezer offers unlimited repairs for a fee of $140 a year plus a $55 service charge for each repair needed. The restaurant’s research suggested that during a given year 85% of these freezers need no repairs, 9% needed to be serviced once, 4% twice, 2% three times, and none required more than three repairs. 
a.	Find the expected number of repairs this kind of freezer is expected to need each year. Show your work. Let Y=number of repairs this kind of freezer needs during a year. Fill in the table:
Y	0	1	2	3	
Prob.					

b.	Find the standard deviation of the number of repairs on one year. 
c.	What are the mean and standard deviation of the restaurant’s annual expense for the service contract? Hint: Write expenses as a function of Y.

3.	(15 pts) The American Red Cross says that about 11% of the U.S. population has Type B blood.  A blood drive is being held at your school.

a.	What is the probability that exactly 3 of the first 15 blood donors have Type B blood?
b.	The blood drive has a total of 160 donors. Assuming this is a typical number of donors for a school blood drive, what would be the mean and standard deviation of the number of donors who have Type B blood?
c.	Surprised by the low number of Type B blood donors at the blood drive, the American Red Cross wonders if the 11% estimate was too high for your area. How many Type B blood donors would it take to convince you that this estimate might be too high? Justify your answer.

4.	(15 pts) It is generally believed that electrical problems affect about 11% of new cars. An automobile mechanic conducts diagnostic tests on 130 new cars on the lot.
a.	Describe the sampling distribution for the sample proportion by naming the model and telling its mean and standard deviation. Justify your answer.
b.	What is the probability that in this group over 14% of the new cars will be found to have electrical problems?

5.	(15 pts) Herpetologists (snake specialists) found that a certain species of reticulated python have an average length of 21.5 feet with a standard deviation of 2.5 feet. The scientists collect a random sample of 36 adult pythons and measure their lengths. In their sample, the mean length was 20 feet long. One of the herpetologists fears that pollution might be affecting the natural growth of the pythons. Do you think this sample result is unusually small? 
a.	Explain what model you will use. 
b.	Check the assumptions for your model.
c.	State the mean and the standard deviation of the sample mean.
d.	What is the probability that the sample mean is at most 20?
e.	Answer the question of the problem: Do you think this sample result is unusually small? 

6.	(25 pts) The countries of Europe report that 46% of the labor force is female. The United Nations wonders if the percentage of females in the labor force is the same in the United States. Representatives from the United States Department of Labor plan to check a random sample of over 10,000 employment records on file to estimate a percentage of females in the United States labor force.
a.	They select a random sample of 530 employment records, and find that 230 of the people are females. State the conditions needed to build a confidence interval.
b.	 They select a random sample of 530 employment records, and find that 229 of the people are females. Create the 98% confidence interval.
c.	Interpret the confidence interval in this context. Explain what 98% confidence means in this context.
d.	Should the representatives from the Department of Labor conclude that the percentage of females in their labor force is lower than Europe’s rate of 46%? Explain.