Probability Questions & Answers

Probability Questions & Answers A baseball team has scheduled its opening game for April 1. If it rains on April 1, the game is postponed and will be played the next day that it does not rain. The team purchases insurance against rain. The policy will pay 1000 for each day, up to 2 days, that the opening game is postponed. The insurance company determines that the number of consecutive days of rain beginning on April 1 is a Poisson random variable with mean 0.6. What is the standard deviation of the amount the insurance company will have to pay? A) 668 B) 699 C) 775 D) 817 E) 904 - ANSWER: 699 A company buys a policy to insure its revenue in the event of major snowstorms that shut down business. The policy pays nothing for the first such snowstorm of the year and $10,000 for each one thereafter, until the end of the year. The number of major snowstorms per year that shut down business is assumed to have a Poisson distribution with mean 1.5. What is the expected amount paid to the company under this policy during a one-year period? A) 2,769 B) 5,000 C) 7,231 D) 8,347 E) 10,578 - ANSWER: 7,231 A company establishes a fund of 120 from which to pay an amount, C, to any of its 20 employees who achieve a high performance level during the coming year. Each employee has a 2% chance of achieving a high performance level during the coming year, independent of any other employee. Determine the maximum value of C for which the probability is less than 1% that the fund will be inadequate to cover all payment for high performance. a) 24 b) 30 c) 40 d) 60 e) 120 - ANSWER: 60 A company prices its hurricane insurance using the following assumptions i) In any calendar year, there can be at most one hurricane. ii) In any calendar year, the probability of a hurricane is 0.05 iii) The number of hurricanes in any calendar year is independent of the number of hurricanes in any other calendar year. Using the company's assumptions, calculate the probability that there are fewer than 3 hurricanes in a 20 years period. a) 0.06 b) 0.19 c) 0.38 d) 0.62 e) 0.92 - ANSWER: .92..................................