Accortime is a manufacturer of quartz crystal watches. Accrotime researchers have shown that the watches have an average life of 37 months before certain electronic components deteriorate, causing the watch to become unreliable. The standard deviation of watch lifetimes is 4.2 months, and the distribution of lifetimes is approximately normal.
a.) If Accortime guarantees a full refund on any defective watch for up to 30 months after purchase, what percentage of total production will the company expect to replace?
b.) If Accortime does not want to make refunds on more than 3.5% of the watches it makes, how long should the guarantee period be rounded to the nearest month?