*45*

For a normally distributed population with a given mean (

**μ**) and standard deviation (**σ**), this calculator finds the value that is needed to be at the x^{th}percentile or higher.For example, suppose the scores on a certain test are normally distributed with a mean of 85 and a standard deviation of 4. We want to know what score a student needs to receive in order to have a higher score than 95% of all other students. This calculator will allow us to find that score.

To find the cut off value for a given population mean, population standard deviation, and percentile, simply fill in the necessary values below and then click the “Calculate” button.

A value of **91.57941** is needed to be above 95% of all other values.

**Explanation:**

z = (X – μ) / σ

1.64485 = (X – 85) / 4

1.64485 * 4 = X – 85

(1.64485 * 4) + 85 = X

**91.57941** = X