The time to failure for a power supply unit used in a particular brand of personal computer (PC) is thought to be exponentially distributed with a mean of 4,000 hours as per the contract between the vendor and the PC maker. The PC manufacturer has just had a warranty return from a customer who had the power supply fail after 2,100 hours of use.
a. What is the probability that the power supply would fail at 2,100 hours or less? Based on this probability, do you feel the PC maker has a right to require that the power supply maker refund the money on this unit?
b. Assuming that the PC maker has sold 100,000 computers with this power supply, approximately how many should be returned due to failure at 2,100 hours or less?