1.Cathy is planning to take the Certified Public Accountant Examination (CPA exam). Records kept by the college of business from which she graduated indicate that57%of students who graduated pass the CPA exam. Assume that the exam is changed each time it is given. Letn= 1, 2, 3, ... represent the number of times a person takes the CPA exam until thefirstpass. (Assume the trials are independent.)

(a) What is the probability that Cathy passes the CPA on the first try? (Use 2 decimal places.)

(b) What is the probability that Cathy passes the CPA exam on the second or third try? (Use 4 decimal places.)

2. In Hawaii, the rate of motor vehicle theft is384thefts per 100,000 vehicles. A large parking structure in Honolulu has issued428parking permits.(a) What is the probability that none of the vehicles with a permit will eventually be stolen? (Roundto 1 decimal place. Use 4 decimal places for your answer.)

(b) What is the probability that at least one of the vehicles with a permit will eventually be stolen? (Use 4 decimal places.)

(c) What is the probability thateightor more vehicles with a permit will eventually be stolen? (Use 4 decimal places.)

3. Records over the past year show that 1 out of335loans made by Mammon Bank have defaulted. Find the probability that1or more out of310loans will default.Hint:Is it appropriate to use the Poisson approximation to the binomial distribution? (Roundto 1 decimal place. Use 4 decimal places for your answer.)

4.Flying over the western states with mountainous terrain in a small aircraft is 40% riskier than flying over similar distances in flatter portions of the nation, according to a General Accounting Office study completed in response to a congressional request. The accident rate for small aircraft in the 11 mountainous western states is2.3accidents per 100,000 flight operations.

(b) Find the probability of no accidents in 100,000 flight operations. (Use 4 decimal places.)

(c) Find the probability of at least7accidents in200,000flight operations. (Use 4 decimal places.)

5.A person with a cough is apersona non grataon airplanes, elevators, or at the theater. In theaters especially, the irritation level rises with each muffled explosion. According to Dr. Brian Carlin, a Pittsburgh pulmonologist, in any large audience you'll hear about12coughs per minute.

(b) Find the probability ofthreeor fewer coughs (in a large auditorium) in a 1-minute period. (Use 4 decimal places.)

(c) Find the probability of at leastsevencoughs (in a large auditorium) in a37-second period. (Use 4 decimal places.)

6. Suppose you are a (junk) bond broker who buys only bonds that have a 50% chance of default. You want a portfolio with at least five bonds that do not default. You can dispose of the other bonds in the portfolio with no great loss. How many such bonds should you buy if you want to be 94.1% sure that five or more bonds will not default?

7.High in the Rocky Mountains, a biology research team has drained a lake to get rid of all fish. After the lake was refilled, they stocked it with an endangered species of Greenback trout. Of the 2000 Greenback trout put into the lake500were tagged for later study. An electroshock method is used on individual fish to get a study sample. However, this method is hard on the fish. The research team wants to know the smallest number of fish that must be electroshocked to be at least50%sure of getting a sample of two or more tagged trout. Please provide the answer. For more studies similar to this one, seeA National Symposium on Catch and Release Fishing, Humboldt State University.---------------fish