According to the National Center for Health Statistics, the life expectancy for a 65-year-old American male is

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According to the National Center for Health Statistics, the life expectancy for a 65-year-old American male is 17.0 years. Assuming that, from age 65, the survival of American males follows an exponential distribution, determine the following probabilities.

(a) The probability that a randomly selected 65-year-old American male will live beyond 80 years of age (at least 15 more years)
(b) The probability that a randomly selected 65-year-old American male will live less than 10 more years

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