1.)State Farm Insurance studies show that in Colorado, 55% of the auto insurance claims submitted for property damage were submitted by males under 25 years of age. Suppose 10 property damage claims involving automobiles are selected at random.

a.) What is the probability that two or more claims are made by males under age 25? (Use 3 decimal places.)


b.) What is the expected number of claims made by males under age 25? What is the standard deviation of the r-probability distribution? (Use 2 decimal places.)

μ
σ

2.)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 lake 400 were 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 least 50% sure of getting a sample of two or more tagged trout. Please provide the answer. For more studies similar to this one, see A National Symposium on Catch and Release Fishing, Humboldt State University.
_______ fish

3.) Records over the past year show that 1 out of 380 loans made by Mammon Bank has defaulted. Find the probability that 4 or more out of 340 loans will default. Hint: Is it appropriate to use the Poisson approximation to the binomial distribution? (Round λ to 1 decimal place. Use 4 decimal places for your answer.)

4.) In Hawaii, the rate of motor vehicle theft is 622 thefts per 100,000 vehicles. A large parking structure in Honolulu has issued 540 parking permits.

(a) What is the probability that none of the vehicles with a permit will eventually be stolen? (Round λ to 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 that two or more vehicles with a permit will eventually be stolen? (Use 4 decimal places.)