Question

Let X be the lifetime of an electronic device. It is known that the average lifetime...

Let X be the lifetime of an electronic device. It is known that the average lifetime of the device is 767 days and the standard deviation is 121 days. Let x¯ be the sample mean of the lifetimes of 157 devices. The distribution of X is unknown, however, the distribution of x¯ should be approximately normal according to the Central Limit Theorem. Calculate the following probabilities using the normal approximation. (a) P(x¯≤754)= Answer (b) P(x¯≥784)= Answer (c) P(749≤x¯≤784)= Answer

Homework Answers

Answer #1
for normal distribution z score =(X-μ)/σx
here mean=       μ= 767
std deviation   =σ= 121.0000
sample size       =n= 157
std error=σ=σ/√n= 9.6569

a)

probability = P(X<754) = P(Z<-1.35)= 0.0885

b)

probability = P(X>784) = P(Z>1.76)= 1-P(Z<1.76)= 1-0.9608= 0.0392

c)

probability = P(749<X<784) = P(-1.86<Z<1.76)= 0.9608-0.0314= 0.9294
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