Question

A recent study of the lifetimes T of cellphones found that the mean is 30 months with a standard deviation of 6 months. A sample of 36 cellphones is randomly selected. If the sample average lifetime is T ̄, find the followings: (a) E(T ̄) = V ar(T ̄) = (b) Distribution of T ̄ ∼ What is the probability that the average lifetime is (c) between 25 and 29 months? (d) more than 36 months?

Answer 1

Solution:

a)

b) Distribution of is:

c) We are required to find:

Using the z-score formula, we have:

  

Now using the standard normal table, we have:

d) We are required to find:

Now using the z-score formula, we have:

Now using the standard normal table, we have: