# Goodness of Fit Problem

#### jessma2006

##### New Member
I am having difficulties on the following problem:

You have a sample of test scores with a mean of 78.2 and a standard deviation of 9.0. To use a goodness of fit test to determine if a sample of scores comes from a normal population, you divide the normal distribution into 10 equal-probability intervals. What score is at the boundary between the upper 20% and the next lower interval?

I am confused how to get started on this problem because the book I am using does not give any examples in which they give a mean and a standard deviation. Any help on how to solve this problem would be appreciated.

#### Mean Joe

##### TS Contributor
I am confused how to get started on this problem because the book I am using does not give any examples in which they give a mean and a standard deviation. Any help on how to solve this problem would be appreciated.
You know how approximately 68% of scores are within 1 standard of deviation from the mean (and how you can use a normal table to find what % are within 2 standards of deviation)? You know about z-scores?

What score is at the boundary between the upper 20% and the next lower interval?
They want you to find the z-score such that 20% of scores are above it; that is z=0.84

To find the x value that corresponds to the z-score, use:
z = (x - mean) / stdev

#### jessma2006

##### New Member
Thank you. I was able to figure it out now.