Question

Accrotime is a manufacturer of quartz crystal watches. Accrotime researchers have shown that the watches have an average life of 30 months before certain electronic components deteriorate, causing the watch to become unreliable. The standard deviation of watch lifetimes is 5 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.)
11.51%

(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)?

Answer 1

As the company guarantees that they will refund the amount if any occurs in the watch within 2 years which means 24 months.

Refer Z-table to find the probability or use excel formula "=NORM.S.DIST(-1.2, TRUE)" to find the probability.

-----------------------------------------------------------------------------------------------------------------

Refer Z-table, Lookup for Z-value corresponding to area 0.06 to the left of the normal curve or use excel formula "=NORM.S.INV(0.06)" to find the Z-value.