Solve the problem.
-Suppose that replacement times for washing machines are normally distributed with a mean of 9.3 years and a standard deviation of 2 years. Find the replacement time that separates the top 18% from the bottom 82%.
A)11.1 years
B)9.7 years
C)10.6 years
D)7.5 years

Question

Quizplus · Accepted Answer

To find the replacement time that separates the top 18% from the bottom 82%, we look for the z-score corresponding to the 82nd percentile in a standard normal distribution. Using a z-table or calculator, the z-score for the 82nd percentile is approximately 0.915. We then use the formula for converting a z-score to an original score: X = μ + zσ, where μ is the mean, σ is the standard deviation, and z is the z-score. Plugging in the values: X = 9.3 + 0.915(2) = 9.3 + 1.83 = 11.13, which rounds to 11.1 years.

Solve the Problem. -Suppose That Replacement Times for Washing Machines Are Normally Distributed