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) The replacement time that separated the top 20% from the bottom 80% is 9.124 years.
(ii. The probability that a randomly selected TV will be replaced in less than 4.0 years is 0.00.
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 for the 80th percentile is 0.84, and 0.84 * 1.1 = 0.924, which is close to 0.9124. (ii) is correct because the z-score for 4.0 years is (4.0 - 8.2) / 1.1 = -3.82, and the probability of a z-score less than -3.82 is very close to 0.

Replacement Times for TV Sets Are Normally Distributed with a Mean