Laptop computers produced by a company have an average life of 38.36 months. Assume that the life of a computer is exponentially distributed (which is a good assumption).
a. What is the probability that a computer will fail within 12 months?
b. If the company gives a warranty period of 12 months, what proportion of computers will fail during the warranty period?
c. Based on the answer to (b), would you say the company can afford to give a warranty period of 12 months?
d. If the company wants not more than 5% of the computers to fail during the warranty period, what should be the warranty period?
e. If the company wants to give a warranty period of three months and still wants not more than 5% of the computers to fail during the warranty period, what should be the minimum average life of the computers?