Suppose that replacement times for washing machines are normally distributed with a mean of 8.6 years and a standard deviation of 1.6 years. Find the replacement time that separates the top 18% from the bottom 82%
The top 18% are in the 82 percentile, so
The Z value for P=0.82 is approximately 0.915 (according to the Z chart)
Therefore, (0.915)(1.6) = 1.464 years above the mean
The bottom 82% are in the 18 percentile, so
Z value for P=0.18 is approximately - 0.915
= 1.464 years below the mean
Therefore the replacement time that separates the top 18% from the bottom 82% is
2(1.464) = 2.9 years
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