Suppose that replacement times for washing machines are normally distributed with a mean of 10.9 years and a standard deviation of 1 years. Find the replacement time that separates the top 18% from the bottom 82%.
A) 11.1 years
B) 10.0 years
C) 11.0 years
D) 11.8 years

Question

Quizplus · Accepted Answer

To find the replacement time that separates the top 18% from the bottom 82%, we need to find the z-score that corresponds to the 82nd percentile of a standard normal distribution. This z-score is approximately 0.915. Using the formula X = μ + zσ, where μ = 10.9 and σ = 1, we calculate X = 10.9 + 0.915(1) = 11.815, which rounds to 11.8 years.

Suppose That Replacement Times for Washing Machines Are Normally Distributed