Suppose that replacement times for washing machines are normally distributed with a mean of 9.5 years and a standard deviation of 1.8 years. Find the replacement time that separates the top 18% from the bottom 82%.

Suppose the replace times for the machines are normally distributed with mean 9.5 years and standard deviation of 1.8 years.

We are required to find the replacement time that separated the top 18% of washing machines from the bottom 82% P (x<82), z=0.9154

but z = (x-mu) / sig

thus

0.9154 (1.8) + 9.5=x

x=11.14772