Question

Accrotime is a manufacturer of quartz crystal watches. Accrotime researchers have shown that the watches have an average life of 35 months before certain electronic components deteriorate, causing the watch to become unreliable. The standard deviation of watch lifetimes is 4 months, and the distribution of lifetimes is normal.

(a) If Accrotime guarantees a full refund on any defective watch for 2 years after purchase, what percentage of total production will the company expect to replace? (Round your answer to two decimal places.)
%

(b) If Accrotime does not want to make refunds on more than 8% of the watches it makes, how long should the guarantee period be (to the nearest month)?
months

Answer 1

Let's consider X be the life times of a watch.

a) Given that Accrotime guarantees a full refund on any defective watch for 2 years(24 months) after purchase.

Therefore the percentage of total production will the company expect to replace is given by

By using z table:

Therefore the percentage of total production will the company expect to replace is 3%

b) If Accrotime does not want to make refunds on more than 8% of the watches it makes, the guarantee period is obtained by:

by using z table:

Therefore the guarantee period should be less than or equal to 29 months.