Accrotime is a manufacturer of quartz crystal watches Accrot

Accrotime is a manufacturer of quartz crystal watches. Accrotime researchers have shown that the watches have an average life of 28 months before certain electronic components deteriorate, causing the watch to become unreliable. The standard deviation of watch lifetimes is 7 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.) Incorrect: Your answer is incorrect. % (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

Solution

For X~N(28, 5^2) a) No refund if it is ok for at least 24 months, P{X>24} = P{Z>z}, where z = (24-28)/5 = 4/5 = - 0.80. P{Z> -0.80} = 1 - P{Z< -0.80} = 1 - 0.2119. Or, % replaced, P{Z< -0.80} = 0.2119, 21%. b) Now, you want P{Z < z} = 0.12, z = - 1.175. But also, z = (x - 28)/5, hence x = 22.125. Take 22 months.