Replacement times for TV sets are normally distributed with a mean of 8.2 years and a standard deviation of 1.1 years, (based on data from "Getting Things Fixed, "Consumer Reports). (i) If you want to provide a warranty so that only 3% of the TV sets will be replaced before the warranty expires, the length of warranty you would recommend would be 6.13 years.
(ii. The probability that a randomly selected TV will be replaced after more than 10.0 years is 0.0505.
A) (i) and (ii) are correct statements.
B) (i) is a correct statement but not (ii).
C) (ii) is a correct statement but not (i).
D) (i) and (ii) are false statements.

Question

Quizplus · Accepted Answer

(i) is correct because the z-score corresponding to a cumulative probability of 0.03 is -1.88, and the corresponding replacement time is 8.2 - 1.88 * 1.1 = 6.13 years. (ii) is correct because the z-score corresponding to a replacement time of 10 years is (10 - 8.2) / 1.1 = 1.64, and the corresponding cumulative probability is 0.0505.

Replacement Times for TV Sets Are Normally Distributed with a Mean