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Problem 4. (15 points) Let X denote the lifetime of a radio, in years, manufactured by a certain company. Assume that the lifetime is exponentially distributed, with a mean of 5 years. (a) (5 points) What is the probability p that a radio lasts more than 15 years? (b) (5 points) What is the (exact) probability that, of 1000 such radios that you purchase, at least four of them last more than 15 years? (You can leave your expression with a “p” in it, where p is the answer from part (a); you do not need to evaluate it) (c) (5 points) Give an alternative expression that approximates your answer to part (b). Justify your answer: What distribution are you using to obtain the approximation?

Name: problem 4 15 points let x denote the lifetime of a radio in years manufactured by a certain company assume that the lifetime is exponentially distributed with a mean of 5 years a 5 points wh 89473
Uploaded: 2023-09-04T08:56:16-08:00
Duration: 2 min 15 s
Channel: Adi S
Description: problem 4 15 points let x denote the lifetime of a radio in years manufactured by a certain company assume that the lifetime is exponentially distributed with a mean of 5 years a 5 points wh 89473

          Problem 4. (15 points) Let X denote the lifetime of a radio, in years, manufactured by a certain company. Assume that the lifetime is exponentially distributed, with a mean of 5 years.
(a) (5 points) What is the probability p that a radio lasts more than 15 years?
(b) (5 points) What is the (exact) probability that, of 1000 such radios that you purchase, at least four of them last more than 15 years? (You can leave your expression with a “p” in it, where p is the answer from part (a); you do not need to evaluate it)
(c) (5 points) Give an alternative expression that approximates your answer to part (b). Justify your answer: What distribution are you using to obtain the approximation?

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