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Provide a step by step solution and be detailed, your handwriting should be readable

(2 points) Suppose a car manufacturer believes its windscreen wipers will last on average for three years on their cars if driven by a typical driver in the province. Moreover, the manufacturer believes the lifetime of the wipers under such conditions is Normally distributed with a standard deviation of two years. Find the probability that, if on a car driven by a typical driver, a windscreen wiper lasts for a time that is not within 1.4 years of the mean lifetime. The probability is:

Explanation / Answer

Mean is 3 and s is 2

We need to find 1-P(-1.4<X<1.4)

thus P(-1.4<x<1.4)

P(x<1.4)-P(x<-1.4)=P(z<(1.4-3)/2)-P(z<(-1.4-3)/2)=P(z<-0.8)-P(z<-2.2) or P(z<2.2)-P(z<0.8) thus from normal distribution it is 0.9861-0.7881=0.198

thus answer is 1-0.198=0.802

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