## 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.

Question

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%.

in progress 0
2 weeks 2021-09-13T07:33:22+00:00 1 Answer 0

Replacement time of 10.064 years.

Step-by-step explanation:

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean and standard deviation , the zscore of a measure X is given by:

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this problem, we have that:

Find the replacement time that separates the top 18% from the bottom 82%.

This is the value of X when Z has a pvalue of 0.82. So it is X when Z = 0.915.

Replacement time of 10.064 years.