FOR INSTRUCTORS USE

a. If a former student is selected at random, find the probability that

I. s/he will be at or above upper middle income given that s/he graduated from college,

II. s/he will be at or above upper middle income given that s/he dropped out from college,

III. s/he will be a college dropout given that s/he is below upper middle income group.

b. Are the events "college graduate" and "below upper middle income" independent? Explain why or why not.

2. A chemical plant has an emergency alarm system. When an emergency situation exists, the alarm sounds with probability 0.95. When an emergency situation does not exist, the alarm system sounds with probability of 0.02. A real emergency situation is a rare event, with probability of 0.004.

a. Draw a tree diagram that summarizes this information

b. What is the probability that alarm will sound?

c. Given that the alarm has just sounded, what is the probability that a real emergency situation exists?

3. The time taken to complete a statistics final by all students is normally distributed with a mean of 120 minutes and a standard deviation of 10 minutes.

a. Find the probability that a randomly selected student will take more than 150 minutes to complete the test.

b. Find the probability that the mean time taken to complete the test by a random sample of 16 students would be between 122 and 126 minutes.

4. Rh-negative blood appears in 15% of the United States population.

a. Find the probability that out of 7 randomly selected U.S. residents at least 3 of them have Rh-negative blood.

b. Use the normal approximation to find the probability that in a group 100 randomly selected people fewer than 17.5% will have a Rh-negative blood.

a. The U.S. Travel Industry estimated that Americans planned to spend an average of 4.8 nights away on vacations in 1995 (U.S. News & World Report, June 12, 1995). Suppose that this mean was based on a random sample of 100 Americans and the population standard deviation was 1.5 nights. Construct a 90% confidence interval for the mean length of vacations Americans planned in 1995.

b. A poll of 1226 adults revealed that 49% believe that the devil may sometimes possess earthlings. Find a 95% confidence interval for the population proportion of the adults who hold this opinion. (Source:"Demons Begone," Asheville Citizen-Times, April 5, 1991).

6. Grocery stores, drugstores, and large supermarkets all use scanners to calculate a customer’s bill. Scanners should be as accurate as possible. A state agency regularly monitors stores by randomly selecting items and comparing with the shelf price with the checkout scanner price. During one check by the agency, 16 items were found to be incorrectly scanned. The amounts of overcharge(in cents) were

200, -99, 100, -50, 40, -60, 20, 30, 50, 300, -120, 100, 50, 30, -70, 40

A negative sign indicates an undercharge-the scanner price was below the shelf price.

7. Do cars traveling in the right lane of I-94 travel slower than those in the left lane? The following sample information was obtained. Use the 0.01 significance level to provide an answer to this question.

8. A noted medical researcher has suggested that a heart attack is less likely to occur among adults who actively participate in athletics. A random sample of 300 adults is obtained. Of that total, 100 are found to be athletically active. Within this group, 10 suffered heart attacks; among the 200 athletically in active adults, 25 had suffered heart attacks.

a. Test the hypothesis that the proportion of adults who are active and suffered heart attacks is different than the proportion of adults who are not active and suffered heart attacks. Use the 0.05 significance level.

b. Construct a 99% confidence interval for the difference between the proportions of all active and inactive adults who suffered heart attacks.

9. Based on interviews of couples seeking divorces, a social worker compiles the following data related to the period of acquaintanceship before marriage and the duration of marriage.