Standard Normal Distribution Calculator

Calculate Z-Score





Formula

To calculate the z-score in a standard normal distribution:

\[ z = \frac{X - \mu}{\sigma} \]

Where:

Standard Normal Distribution Definition

The standard normal distribution is a normal distribution with a mean of 0 and a standard deviation of 1. It is used to determine the probability of a random variable falling within a certain range under the standard normal curve. The z-score represents the number of standard deviations a data point is from the mean, allowing for the comparison of different datasets on a standardized scale.

Example Calculation 1

Let's assume the following values:

Using the formula:

\[ z = \frac{75 - 70}{5} = 1.0000 \]

The standard normal distribution (z-score) is 1.0000.

Example Calculation 2

Let's assume the following values:

Using the formula:

\[ z = \frac{50 - 45}{10} = 0.5000 \]

The standard normal distribution (z-score) is 0.5000.