Question

8. -/11.11 POINTS BBBASICSTAT8 7.3.030.MI. MY NOTES ASK YOUR TEACHER Accrotime is a manufacturer of quartz crystal watches. Accrotime researchers have shown that the watches have an average life of 26 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 12% of the watches it makes, how long should the guarantee period be (to the nearest month)? months Need Help? Read It Master It Talk to a Tutor

Answer 1

-Аю 1 = 26 months , o= 4 months XUN14,02) @ P{ xE2 Years] = P { x < 24 months] = P[ X-4s 24-47 IPL za 24-261 = P(Z <-05] = 1-P [Z <0.5] mop[Z <0-5) = 016915 (From Z-table) P[z<-05)= 1-0.6915= 0.3085 P[ X3 2 Years]=0.3005] -0.5 The percentage of the total production will be replaced if Accortime guarantees a full refund on any defective watch for 2years after purchase is 30.05% p= 1207 Zup = Z or= -1.17 (From z-table) X = tzo = 26+ (-1.17 x 4) = 21.32 txz 21 months If Accorti me does not want to refunds 12% of watches it makes, : guarantee period should be 21 months more than the