Question

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 5 months, and the distribution of lifetimes is normal.

a) If Accorotime guarantees a full refund on any defective watch for 2 years after purchase, what percentage of total production should the company expect to replace?

b0 If Accorotime does not want to make refunds on more than 12% of the watches it makes, how long should the guarantee period be ( to the nearest month)? Given info:     

Answer 1

Let X represents the distribution of life times and it follows the normal distribution with parameters (μ-28months, σ 5 months) a) Determine the percentage of total production should the company expect to replace Consider that Accorotime guarantees a full refund on any defective watch for 2 years (24 months) after purchase P(X < 24) = P(X-μ <24-28 P(Z <-0.8) Φ(-0.8 = 0.2119 ~ 21.19% Use the Excel function, NORMSDIST(a) Therefore, the percentage of total production should the company expect to replace is 21.19% b) Consider that Accor°time does not want to make refunds on more than 12% of the watches P(X < x) = 0.12 X-μ x-28 ZKx-28) =(-NORMSINV(0.12)) ( Use Excel function) x 28 x=-1.1750(5) +28

x=22.1251 Therefore, 22 months period should be guarantee.