1 Consider the experiment of selecting a playing card from a deck of 52 playing cards. Each card corresponds to a sample point with a probability. 52 (a) List the sample points in the event a queen is selected. Os = {x | x is a card from the deck that is not a spade a club or a diamond} S = {x | x is a card from the deck but not king, ace, or jack} S = {king of clubs, king of diamonds, king of hearts, king of spades} S = {12 of clubs, 12 of diamonds, 12 of hearts, 12 of spades} S = {queen of clubs, queen of diamonds, queen of hearts, queen of spades} (b) List the sample points in the event a spade is selected. S = {1 of spades, 2 of spades, ..., 10 of spades, 11 of spades, 12 of spades, 13 of spades} S = {x | x is a card from the deck but not a diamond or a heart} S = {2 of spades, 3 of spades, ..., 10 of spades, jack of spades, queen of spades, king of spades, ace of spades} S = {2 of spades, 3 of spades, ..., 9 of spades, 10 of spades, jack of spades, queen of spades, king of spades} S = {2 of clubs, 3 of clubs, ..., 10 of clubs, jack of clubs, queen of clubs, king of clubs, ace of clubs} (c) List the sample points in the event a face card (jack, queen, or king) is selected. Os = {jack of clubs, jack of diamonds, jack of hearts, jack of spades, queen of clubs, queen of diamonds, queen of hearts, queen of spades, king of clubs, king of diamonds, king of hearts, king of spades} S = {11 of clubs, 11 of diamonds, 11 of hearts, 11 of spades, 12 of clubs, 12 of diamonds, 12 of hearts, 12 of spades, 13 of clubs, 13 of diamonds, 13 of hearts, 13 of spades} S = {x | x is a card from the deck that is not numbered} S = {jack of hearts, queen of spades, king of clubs} S = {jack of clubs, queen of clubs, king of clubs, jack of hearts, queen of hearts, king of hearts, jack of spades, queen of spades, king of spades, jack of clubs, queen of clubs, king of clubs} (d) Find the probabilities associated with each of the events in parts (a), (b), and (c). (Enter your probabilities as fractions.) For (a): For (b): For (c): The probability distribution for the random variable x follows. x f(x) 20 0.25 25 0.10 30 0.30 35 0.35 (a) Is this probability distribution valid? Explain. Since f(x) ? 0 for all values of x and f(x) = = this ---Select--- a proper probability distribution. (b) What is the probability that x = 30? (c) What is the probability that x is less than or equal to 25? (d) What is the probability that x is greater than 30? 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 1,000 0.04 3,000 0.03 5,000 0.02 8,000 0.01 10,000 0.01 (a) Use the expected collision payment to determine the collision insurance premium (in dollars) that would enable the company to break even. (b) The insurance company charges an annual rate of $520 for the collision coverage. What is the expected value of the collision policy (in dollars) 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? expected value of the policy = $ You may need to use the appropriate appendix table or technology to answer this question. Consider a binomial experiment with n = 10 and p = 0.20. (a) Compute f(0). (Round your answer to four decimal places.) f(0) = (b) Compute f(2). (Round your answer to four decimal places.) f(2) = (c) Compute P(x < 2). (Round your answer to four decimal places.) P(X 2) = (d) Compute P(x 1). (Round your answer to four decimal places.) P(x 1) = (e) Compute E(X). E(x) = (f) Compute Var(x) and . (Round your answer for to two decimal places.) Var(x) = You may need to use the appropriate appendix table or technology to answer this question. Emergency 911 calls to a small municipality in Idaho come in at the rate of one every two minutes. (a) What is the expected number of calls in one hour? (b) What is the probability of three calls in five minutes? (Round your answer to four decimal places.) (c) What is the probability of no calls in a five-minute period? (Round your answer to four decimal places.) Axline Computers manufactures personal computers at two plants, one in Texas and the other in Hawaii. The Texas plant has 45 employees; the Hawaii plant has 15. A random sample of 10 employees is to be asked to fill out a benefits questionnaire. (Round your answers to four decimal places.) (a) What is the probability that none of the employees in the sample work at the plant in Hawaii? (b) What is the probability that 1 of the employees in the sample works at the plant in Hawaii? (c) What is the probability that 2 or more of the employees in the sample work at the plant in Hawaii? (d) What is the probability that 9 of the employees in the sample work at the plant in Texas?