Question:

A manufacturer of squash racquets has collected information on time in months to breakage for their racquets in normal play; that is, not due to mishandling. Data from past records on breakages suggest an average of 17.5 months and a standard deviation of 6.2 months.

Assume a normal distribution of time to breakage.

a) What proportion of racquets last at least two years?

b) The manufacturer offers a guarantee period in which racquets breaking in normal playing conditions are replaced. What guarantee period should be set if it is desired to limit the probability of replacing a racquet to 0.01?

c) Racquets can be bought in packs of two. Assuming that the second racquet is not used until the first is broken, what proportion of packs last at least four years?

d) The manufacturer offers to replace a pack if both racquets break in less than a guarantee period. What period should be set to limit the probability of replacing a pack to 0.01?