Because of the symmetrical nature of the normal curve, we can use a special rule, known as the empirical rule.

Key Concepts: The *Empirical Rule*
The empirical rule states that approximately: 68% of the results are within one standard deviation of the mean; 95% of the results are within two standard deviations of the mean; 99.7% of the results are within 3 standard deviations of the mean.

Record the Key Concepts information above into your notebook. Then, consider how we might use the Empirical Rule to solve problems like example 1 below. When you are ready, click the play button below to view the video explanation.

Example 1: The mean height of baseball players is 70 inches, with a standard deviation of 4.5 inches.

(a) Draw the distribution. Label the mean and 3 standard deviations above and below the mean.

(1) Start by making the normal curve, label the mean, and draw three marks above and below the mean.

a normal distribution with 70 labeled as the mean

(2) Use the standard deviation to add values above and below the mean.

a normal distribution with the mean and 3 standard deviations shown on either side

(b) Fill in the blanks.

68% of the players have a height between _____ and _____.

95% of the heights are between _____ and _____.

99.7% of the heights are between _____ and _____.

Try example 2 in your notebook. We'll provide a little less help this time.

Example 2: All UT freshmen take a entry math test. The scores were normally distributed with a mean of 75 and a standard deviation of 4.

(a) Draw the distribution. Label the mean and 3 standard deviations above and below the mean.

(b) Fill in the blanks.

68% of the scores are between _____ and _____.

95% of the scores are between _____ and _____.

99.7% of the scores are between _____ and _____.

View the sample solution and compare it to yours.

Remember, the empirical rule works for any normal distribution! Remember, 68%...95%...and 99.7%.

These images adapted from OpenStax College. Download for free at http://cnx.org/contents/30189442-6998-4686-ac05-ed152b91b9de@18.13