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Suppose a battery has a useful life described by the exponential distribution with a mean of 500 days

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Suppose a battery has a useful life described by the exponential distribution with a mean of 500 days.

(a) What is the probability that it will fail before its expected lifetime?

(b) If a battery has a 12-month (365-day) warranty, what is the probability that it will fail during the warranty period?

(c) What is the probability that a battery which has lasted 365 days will operate beyond its expected lifetime?