Normal Distribution

Question

Suppose that replacement times for washing machines are normally distributed with a mean of 10 years and a standard deviation of 1.4 years. Find the replacement time that separates the top 18% from the bottom 82%

 

Any help with explaining the steps to solve this would be greatly appreciated.

 

Thank you,

Tammi

Answer 1

Obtain a z-score chart:

http://www.utdallas.edu/dept/abp/zscoretable.pdf

 

For 82% the z-score is 0.915

 

z = (X - μ) / σ

 

0.915 = (X - 10) / 1.4         multiply both sides by 1.4

1.281 = X - 10                    add 10 to both sides

11.281 = X

 

A replacement time of 11.281 years separates the top 18%.

 

Answer 2

You would use the formula z=(x-μ)/σ

 

You are given μ=10 and σ=1.4

 

You are looking for the value of x therefore you need the value of z.

 

For that you will need to look at a normal distribution table.

 

You want the value of z that gives the area=.32 under the normal curve from 0 to that value.