Consumer Reports indicated that the average life of a refrigerator before replacement is 14 years with a standard deviation of 2.5 years. Let X be the age at which a refrigerator is replaced. Assume that X has a distribution that is approximately normal. Suppose the company wants to set the warranty period so that it does not have to replace more than 2.5% of the refrigerators under guarantee. Required:
a. State the random variable.
b. What is the probability that someone will keep a refrigerator fewer than 11 years before replacement?
c. What is the probability that someone will keep a refrigerator more than 18 years before replacement?
d. What is the probability that someone will replace a refrigerator between 8 and 15 years?