The probability distribution for damage claims paid by the Newton Automobile Insurance Company on collision insurance follows:

Payment ($)	Probability
0	0.85
500	0.04
1000	0.04
3000	0.03
5000	0.02
8000	0.01
10000	0.01

1. (5 points) Use the expected collision payment to determine the collision insurance premium that would enable the company to break even. Show your calculation

2. (5 points) The insurance company charges an annual rate of $520 for the collision coverage. What is the expected value of the collision policy for a policyholder? (Hint: It is the expected payments from the company minus the cost of coverage). Why does the policy holder purchase a collision policy with this expected value?

The broadcast networks introduce new TV shows each fall. In an attempt to get viewers interested in the new shows, TV commercials are aired during the summer as part of a promotional campaign conducted prior to the fall debuts. The networks then conduct surveys to see what percentage of the viewing public is aware of the shows. According to network sources, in the fall of 2015, 68% of viewers aged 18-49 were aware of the new series Blindspot. Suppose that a random sample of 10 viewers aged 18-49 is selected.

3. (5 points) MINITAB Probability Distribution (must be included to receive credit for 4 - 6).

4. (5 points) What is the probability that less than three of the viewers are aware of Blindspot?

5. (5 points) What is the probability that 5 or more are aware of Blindspot?

6. (5 points) What is the probability that all 10 are aware of Blindspot?

More than 50 million guests stayed at bed and breakfasts (B & Bs) last year. The Web site for the Bed and Breakfast Inns of North America, which average approximately seven visitors per minute, enables many B & Bs to attract guests without waiting years to be mentioned in guidebooks. (Hint: make sure you know l for each question)

7. (5 points) Determine the probability of no Web site visitors in a one-minute period.

8. (5 points) Determine the probability of one or more Web site visitors in a 30-second period.

Suppose that a machine shop orders 500 bolts from a supplier. To determine whether to accept the shipment of bolts, the manager of the facility randomly selects 12 bolts. If none of the 12 randomly selected bolts is found to be defective, he concludes that the shipment is acceptable.

9. (10 points) If 10% of the bolts in the population are defective, what is the probability that none of the selected bolts are defective? Use MINITAB and include output

In the classic movie Forrest Gump, the public school required an IQ of at least 80 for admittance.

10. (5 points) If IQ test scores are normally distributed with mean 100 and standard deviation 16, what percentage of people would qualify for admittance to the school? Show your calculation

11. (5 points) If the public school wishes 95 percent of all children to qualify for admittance, what minimum IQ test score should be required for admittance? Show your calculation

Jim Sears manufactures farm equipment. His work requires the use of steel bars which must have a mean length of at least 50 inches. The bars can be purchased from a supplier in Kansas City whose bars average only 47 inches with a standard deviation of 12 inches, or from a supplier in Dallas whose bars average 49 inches with a standard deviation of 3.6 inches.

12. (8 points) If Sears is to buy 81 bars from Kansas City, what is the probability they will have a mean of at least 50 inches? Show your calculation

13. (8 points) If Sears is to buy 81 bars from Dallas, what is the probability they will have a mean of at least 50 inches? Show your calculation

14. (4 points) Should he use the supplier in Kansas City or the supplier in Dallas? Explain

The Grocery Manufacturers of America reported that 76% of consumers read the ingredients listed on a products label. Assume the population proportion is p = .76 and a sample of 400 consumers is selected from the population.

15. (10 points) What is the probability that the sample proportion will be within .03 of the population proportion? Show your calculation

16. (5 points) If the sample of 400 was made up of 50 adults randomly selected from each of the eight regions of the U.S. (i.e. New England, Midwest, Great Lakes, Plains, Southeast, Southwest, Rocky Mountain and Far West) which sampling design was used?

17. (5 points) If repeated random samples of size 400 are taken from an infinite population, the distribution of sample proportions will be ______ ______ because of the ______ ______ ______.