2.2.7  The Empirical Rule
2.2.7  The Empirical RuleA normal distribution is symmetrical and bellshaped.
The Empirical Rule is a statement about normal distributions. Your textbook uses an abbreviated form of this, known as the 95% Rule, because 95% is the most commonly used interval. The 95% Rule states that approximately 95% of observations fall within two standard deviations of the mean on a normal distribution.
 Normal Distribution
 A specific type of symmetrical distribution, also known as a bellshaped distribution
 Empirical Rule

On a normal distribution about 68% of data will be within one standard deviation of the mean, about 95% will be within two standard deviations of the mean, and about 99.7% will be within three standard deviations of the mean
 95% Rule
 On a normal distribution approximately 95% of data will fall within two standard deviations of the mean; this is an abbreviated form of the Empirical Rule
Example: Pulse Rates
Suppose the pulse rates of 200 college men are bellshaped with a mean of 72 and standard deviation of 6.
 About 68% of the men have pulse rates in the interval \(72\pm1(6)=[66, 78]\).
 About 95% of the men have pulse rates in the interval \(72\pm2(6)=[60, 84]\).
 About 99.7% of the men have pulse rates in the interval \(72\pm 3(6)=[54, 90]\).
Example: IQ Scores
IQ scores are normally distributed with a mean of 100 and a standard deviation of 15.
 About 68% of individuals have IQ scores in the interval \(100\pm 1(15)=[85,115]\).
 About 95% of individuals have IQ scores in the interval \(100\pm 2(15)=[70,130]\).
 About 99.7% of individuals have IQ scores in the interval \(100\pm 3(15)=[55,145]\).