Solve the problem. Round to the nearest tenth unless indicated otherwise.
-Suppose that replacement times for washing machines are normally distributed with a mean of 8.4 years and a standard deviation of 2 years. Find the replacement time that separates the top 18% from the bottom 82%.
A) 6.6 years
B) 9.7 years
C) 8.8 years
D) 10.2 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. Using a standard normal distribution table or calculator, the z-score for 0.82 is approximately 0.915. Using the formula X = μ + zσ, where μ = 8.4 and σ = 2, we get X = 8.4 + 0.915(2) = 10.23, which rounds to 10.2 years.

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