Accrotime is a manufacturer of quartz crystal watches. Accrotime researchers have shown that the watches have an average life of 32 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.

Question

(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 16% of the watches it makes, how long should the guarantee period be (to the nearest month)?

Answer 1

From the problem statement, N(32, 7).

(A)
2 years is equivalent to 24 months. We want to know how many watches will break on average.
P(X < 24) = .1265 = 12.65% (ouch)

(B)
This statement asks that we modify the warranty so that less than 16% of watches are refunded. We use our handy-dandy inverse norm function to calculate the z-score associated with this.

z = -.994 = (x - mu) / sigma

With a little algebra, we get
x = (-.994 * sigma) + mu
x = (-.994 * 7) + 32
x = 25.03 months

This answer makes sense because we know that ~12% of watches break within 24 months.