The lifetime of a new stereo is estimated to be 12 years wit

The lifetime of a new stereo is estimated to be 12 years with a standard deviation of 2.5 years.

A. What is the probability of the stereo failing after 4 years?

B. If there is a full replacement guarantee of 3.5 years, What is the expected proportion of replacements?

C. If the firm is willing to replace up to 3%, What guarantee period should it specify?

Please show your work

The data is as follows,

Expected lifetime of a new sterio = 12 years

Standard deviation = 2.5 years

Probability that the sterio would fail after 4 years = (12 - 4)/2.5 = 8/2.5 = 3.2

Find P(Z=3.2) = 0.4993

Hence, there is 50% probability that the sterio would fail after 4 years.