Question

Assume that a set of test scores is normally distributed with a mean of 100 and a standard deviation of 20. What is the percentage of scores between 80 and 140?

Answer 1

`81.5%` of the score are between `80` and `140`.

Explanation:

We know that the standard deviation is `20` and the mean is `100`. That means `80` is one SD away from the mean. `140` is two SD away from the mean in the other direction.

• `34%` fall between `80` and `100`
• `34%` fall between `100` and `120`
• `13.5%` fall between `120` and `140`

Therefore,

`34% + 34% + 13.5% = 81.5%`