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Math425hw4 - SPRING 2009 MATH 425 Ralf Spatzier Homework 4...

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SPRING 2009 MATH 425 Ralf Spatzier Homework 4 for Friday, June 5 (1) Suppose X is a normal random variable with mean 5. If P ( { X > 9 } ) = . 2, approxi- mate what is V ar ( X ). (2) In 10,000 independent tosses of a coin, the coin lands heads 5800 times. Is it reason- able to assume that the coin is not fair? Explain. (3) The number of years that a radio functions is exponentially distributed with param- eter λ = 1 8 . If Jones buys a used radio what is the probability that it still functions after 8 years? (4) Each item produced by a company is, independently, of acceptable quality with probability .95. Approximate the probability that at least 10 of the next 150 items produced are unacceptable. (5) If X is an exponential random variable with parameter λ , and c > 0 show that cX is exponential with parameter λ/c . (6) At a bank, the amount of time a teller spends with a customer is an exponential random variable with mean 5 minutes. If there is a customer in service when you
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