Question

3. Whirlaway claims that the useful lifetime of its dishwashers is normally distributed with a mean of three years and a standard deviation of one year. Department of Economics Economics 272 Occidental College Professor Williams

a. If the firm guarantees its machines for one year, what fraction will break down within the warranty period? Sketch the distribution of dishwasher life and indicate clearly how your answer shows up in the graph.

b. What fraction will break down within two years?

c. If it costs Whirlaway $250 to fix a guaranteed dishwasher, how much do they have to add to the price of a dishwasher to cover (on average) the cost of the warranty? Explain.

d. Consumer Rejects magazine tested two of Whirlaway’s machines for two years and found that both broke down. If Whirlaway’s claims are correct, what is the probability that two tested machines will both break down in less than two years? Does this probability calculation cast some doubt on Whirlaway’s claims? (Hint: If A and B are two independent events, the probability of both A and B occurring is equal to the product of the probabilities of the individual events – i.e., P(A)P(B).)

Answer 1

Given that the useful lifetime of its dishwashers is normally distributed with a mean of three years and a standard deviation of one year .

a) The probability,

b) The probability,

c) The amount they have to add to the price of a dishwasher to cover (on average) the cost of the warranty is

d)  The probability that two tested machines will both break down in less than two years is

Since the above probability is very low, this probability calculation does not cast some doubt on Whirlaway’s claim.