Reports indicated that the average life of a refrigerator before replacement is m 5 14 years with a (95% of data) range from 9 to 19 years. Let x 5 age at which a refrigerator is replaced. Assume that x has a distribution that is approximately normal.

(a) Find a good approximation for the standard deviation of x values. Hint: See Problem 31.

(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) Inverse Normal Distribution Assume that the average life of a refrigerator is 14 years, with the standard deviation given in part (a) before it breaks. Suppose that a company guarantees refrigerators and will replace a refrigerator that breaks while under guarantee with a new one. However, the company does not want to replace more than 5% of the refrigerators under guarantee. For how long should the guarantee be made (rounded to the nearest tenth of a year)?