Stats 1 The life of a certain type of automobile tire is nor

The life of a certain type of automobile tire is normally distributed with mean 34000 miles and standard deviation 4000 miles. c. Find the probability that 2 out of 5 randomly selected tires will have lifetime 1.96 standard deviations above the mean.

Solution

as you reuire only part c. only answer of part c is provided.

let X be the random variable denoting the life of a certain type of automobile tire.

by question X~N(34000,4000²)

so 1.96 standard deviation above the mean is=34000+1.96*4000=41840

now P[X>41840]=1-P[X<41840] where X~N(34000,4000²)

using minitab we get P[X>41840]=1-0.975002=0.025

let Y be the random variable denoting the number of tires out of 5 tires have lifetime 1.96 standard deviations above the mean.

hence Y~Bin(5,P[X>41840]=0.025)

so P[Y=2]=⁵C₂0.025²(1-0.025)^5-2=0.0057929 [answer]