Normal Distribution

The normal distribution is a continuous probability distribution. In a continuous probability distribution, a continuous random variable can assume an uncountable number of possible values. Some examples are time, height, weight, salary, and IQ.

A normal distribution

• is bell-shaped;
• is symmetric around the mean; and
• has the same mean, median, and mode.

The variable ($\chi$) can take any value between. The mean ( $\mu$) and standard deviation ( $\sigma$) of the normal distribution tell us the shape of a normally distributed curve. As long as we know these two, we can use the values to compute probability that the variable will be above or below a certain value. We will discuss this shortly. First, let's see which variables are normally distributed.

 

When Is the Normal Distribution Applicable?

A bell-shaped histogram usually shows up when variation in the data is primarily caused by small variations in a large number of independently operating contributing sources of variation. Here are a few examples:

The following possibly will not be represented by normal curve:

• weekly sales of branded material (big variations may be caused by advertising, holiday season, etc.)
• home values (big variations are caused by location, square footage, number of bedrooms)