a2s - MATH 1131 3.0 - Fall 2011 Assignment 2 (Due Date: Oct...

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MATH 1131 3.0 - Fall 2011 Assignment 2 (Due Date: Oct 19, 2011) (hand in all questions) Question 1: Suppose that in a weekly lottery you have probability .02 of winning a prize with a single ticket and that you buy 1 ticket per week for 52 weeks. a. (2 marks) What is the probability that you win no prizes? b. (2 marks) What is the probability that you win 3 or more prizes? c. (2 marks) What is the mean and standard deviation of the number of prizes you win? Solution: Let X be the number of weeks that you win; then X is a binomial rv with n = 52 and p = 0 . 02. (a) P(X=0) = 0.350; (b) P ( X 3) = 1 - P ( X 2) = 1 - P ( X = 0) - P ( X = 1) - P ( X = 2) = 0 . 0859. (c) E(X) = 52(0.02) = 1.04; Standard deviation of X = q 52(0 . 98)(0 . 02) = 1 . 0192 = 1 . 01. Question 2: An appliance dealer sells three different models for upright freezers have 13.5, 15.9, and 19.1 cubic feet of storage space, respectively. Let X = the amount of storage space purchased by the next customer to buy a freezer. Suppose that X has the following probability distribution: X 13.5 15.9 19.1 P ( X = x ) .2 .5 .3 a. (3 marks) Find the mean and standard deviation of X. b. (3 marks) If the price of the freezer depends on the size of the storage space, X, such
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a2s - MATH 1131 3.0 - Fall 2011 Assignment 2 (Due Date: Oct...

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