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 0.40.
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 it uses the concept of z-scores to find the cutoff point for the top 20% in a normal distribution, which can be calculated using the mean and standard deviation provided. (ii) is incorrect because the probability of a TV being replaced in less than 4.0 years would be very low given the mean of 8.2 years and standard deviation of 1.1 years; a z-score calculation or lookup in a normal distribution table would show a probability much lower than 0.40.

Replacement Times for TV Sets Are Normally Distributed with a Mean