If a shipment of 30,000 batteries is assumed to have a lifetimes which are normally distributed with mean 360 days and standard deviation 25 days what percentage could be expected to last more than 365 days?
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Expert's answer
2011-10-07T09:00:23-0400
Let X be the random variable equal to the lifetime of a battery. Then by assumption it has normal distribution with mean 360 days and standard deviation 25 days. We have to find the probability P(X>365).
Notice that the random variable Y=(X-360)/25 has normal distribution with mean 0 days and standard deviation 1, and the values of its probabilities is known from tables. Therefore P(X>365) = P( (X-360)/25 > (365-360)/25 ) = P( Y > 5/25 ) = P(Y>0.2) = 1 - P(Y<0.2) = = 1 - F^{-1}(0.2) = = 1 - 0,5792597094 = = 0,4207402906
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