3. Downhill Ski Resort in Colorado has accumulated information from records of the past 30 winters regarding the measurable snowfall. This information is as follows:
Snowfall (in.) Frequency
a. Determine the probability of each event in this frequency distribution.
b. Are all the events in this distribution mutually exclusive? Explain.
33. The SAT scores of all freshmen accepted at State University are normally distributed, with a mean of 1,050 and a standard deviation of 120. The College of Business at State University has accepted 620 of these freshmen into the college. All students in the college who score over 1,200 are eligible for merit scholarships. How many students can the college administration expect to be eligible for merit scholarships?
15. A machine shop owner is attempting to decide whether to purchase a new drill press, a lathe, or a grinder. The return from each will be determined by whether the company succeeds in getting a government military contract. The profit or loss from each purchase and the probabilities associated with each contract outcome are shown in the following payoff table:
Purchase Contract .04 No Contract .06
Drill press $40,000 $−8,000
Lathe 20,000 4,000
Grinder 12,000 10,000
Compute the expected value for each purchase and select the best one
19. The financial success of the Downhill Ski Resort in the Blue Ridge Mountains is dependent on the amount of snowfall during the winter months. If the snowfall averages more than 40 inches, the resort will be successful; if the snowfall is between 20 and 40 inches, the resort will receive a moderate financial return; and if snowfall averages less than 20 inches, the resort will suffer a financial loss. The financial return and probability, given each level of snowfall, follow:
Snowfall Level (in.) Financial Return
> 40, .4 $120,000
20−40, .2 40,000
< 20, .4 − 40,000
A large hotel chain has offered to lease the resort for the winter for $40,000. Compute the expected value to determine whether the resort should operate or lease. Explain your answer.