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STT 231 Test 3 RED Give your answer in the scantron provided Each question is worth 2 points 1 Six Republicans and four Democrats have applied for two open positions on a planning committee Since all the applicants are qualified to serve the City Council decides to pick the two new members randomly What is the probability that both come from the same party A 42 90 B 42 100 C 52 90 D 66 90 E 52 90 2 Which of these has a binomial model A The colors of the cars in the grocery store parking lot B The number of black cards in a well shuffled deck of cards C The number of people we survey until we find someone who owns an iPod D The number of cards drawn from a deck until we find all four aces E The number of hits a baseball player gets in 6 times at bat 3 Pepsi is running a sales promotion in which 12 of all bottles have a FREE logo under the cap What is the probability that you find two free ones in a 6 pack A 1 B 97 C 23 D 13 E 11 4 Let Y be a random variable that takes values 1 0 1 2 with probabilities 3C 0 4 2C and 0 1 respectively If the table is a probability distribution table find the value of C Y P Y A 0 10 1 3C 0 0 4 B 0 15 1 2C 2 0 1 C 0 20 D 0 25 5 Let X be a random variable with probability distribution table given below X P X 2 0 36 1 0 04 What is the probability that X takes a positive value A 0 30 B 0 15 6 The function f x 3x 2 1 x 2 is a density function A True B False 0 0 3 C 0 20 1 0 16 2 0 14 D 0 6 7 A new medicine has an 65 success rate Five patients are treated with it Each patient s conditions improves worsens independent of the other patients You want to compute the probability that exactly four of the five patients are cured What probability model will you use for this A The exponential probability model B The uniform probability model C The hypergeometric probability model D The capture recapture model E The binomial probability model 8 In a box there are 10 red balls and 10 green balls You select three balls without replacement To calculate the