Question

Accrotime is a manufacturer of quartz crystal watches. Accrotime researchers have shown that the watches have an average life of 36 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 6% of the watches it makes, how long should the guarantee period be (to the nearest month)? months

Answer 1

a) The z score for 2 years that is 24 months is computed here as:

Given that Accrotime guarantees a full refund on any defective watch for 2 years after purchase, therefore the probability of a full refund is computed here as:
= P(Z < -3)

Getting it from the standard normal tables, we get here:

P(Z < -3) = 0.0013

Therefore 0.13% of total production will the company expect to replace

b) From standard normal tables, we have here:
P(Z < -1.555) = 0.06

Therefore the guarantee period in months here is computed as:
= Mean -1.555*Std Dev

= 36 -1.555*4

= 29.78

Therefore 29.78 months is the required guaranteed period here.