Normal distribution:
A normal distribution — sometimes called the bell curve — is a statistical distribution that occurs naturally in many situations, like the spread of data for a college test. In this college test example, the bulk of students will score the average (C), while smaller numbers of students will score a B or D and an even smaller percentage of students score an F or an A. this creates a distribution that resembles a bell (hence the nickname the bell curve). The bell curve is symmetrical — half of the data will fall to the left of the mean and half of the later will fall to the right.Many data groups follow a Normal Distribution pattern:
- heights of people
- measurement errors
- blood pressure
- points on a test
- IQ scores
- salaries
- 68% of the normal distribution falls within one standard deviation of the mean.
- 95% of the normal distribution falls within two standard deviations of the mean.
- 99.7% of the normal distribution falls within three standard deviations of the mean.standard normal distribution
Spread of the normal distribution
The standard deviation controls the spread of the normal distribution. A smaller standard deviation means that the data is more concentrated and the bell curve will be taller; a larger standard deviation means that the data is spread out, resulting in a flatter, wider bell curve.
The Normal Distribution and Z-scores
The probability of a random event occurring in a normal distribution (for example, the probability of you scoring a 100 on a test) can be determined by consulting a z-table, which has a mean of 0 and a standard deviation of 1. To use the z-table, you must convert your data to have a mean of 0 and standard deviation of 1 by using the z-formula. This site has a series of articles that explain how to solve normal distribution word problems and how to use the z-formula.
