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Unformatted text preview: 0.1 Exercises for Chapter 3 Part II 1. Suppose 10% of all components manufactured at General Electric are defective, what is the probability that among 15 randomly chosen components that (a) exactly 3 are defective? Calculate using the probability mass function. (b) between 2 and 5 inclusive are defective? Calculate using the tables of the cumulative distribution function. (c) exactly 12 are not defective? (d) How many of the next 15 components would you expect to be defective? 2. On average, 50 out of 100 letters are delivered within 2 working days. You send out 20 letters on Wednesday to invite friends for dinner. Only those who receive the invitation by Friday (i.e., within 2 working days) will come. Let X denote the number of friends who come to dinner. (a) The distribution of the random variable X is (choose one) (i) binomial (ii) hypergeometric (iii) negative binomial (iv) Poisson (b) What is the expected value of X ? (c) Determine the probability that at least 6 friends are coming. (d) A catering service charges a base fee of $100 plus $10 for each guest coming to the party. What is the expected value of the total catering cost? 3. In a shipment of 10 electronic components, 2 are defective. Suppose that 5 com- ponents are selected at random for inspection, and let X denote the number of defective components found. a) The distribution of the random variable X is (choose one) (i) binomial (ii) hypergeometric (iii) negative binomial (iv) Poisson b) Find the probability mass function of X . c) Find the mean value and variance of X . 1 4. Suppose that 30% of all drivers stop at an intersection having flashing red lights when no other cars are visible. Of 20 randomly chosen drivers coming to an inter- section under these conditions, let X denote the number of those who stop. a) The distribution of the random variable X is (choose one) (i) binomial (ii) hypergeometric (iii) negative binomial (iv) Poisson b) Find the probabilities P ( X = 6) and P ( X 6). c) Find 2 X . 5. Three electrical engineers toss coins to see who pays for coffee. If all three match, they toss another round. Otherwise the odd person pays for coffee. (a) Find the probability that a round of tossing will result in a match (that is, either three heads or three tails). (b) Find the probability that they will have to toss more than two times to deter- mine an odd person. 6. A telephone operator receives calls at a rate of 0 . 3 per minute. Let X denote the number of calls received in a given 3-minute period....
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