Question

Suppose the data have a bell-shaped distribution with a mean of 20 and a standard deviation of 5. Use the empirical rule to determine the percentage of data within each of the following ranges:

a. Within one standard deviation of the mean (15 to 25)

b. Within two standard deviations of the mean (10 to 30)

c. Within three standard deviations of the mean (5 to 35)

Answer 1

Suppose the data have a bell-shaped distribution with a mean of 20 and a standard deviation of 5. Use the empirical rule to determine the percentage of data within each of the following ranges:

a. Within one standard deviation of the mean (15 to 25)

b. Within two standard deviations of the mean (10 to 30)

c. Within three standard deviations of the mean (5 to 35)

Answer 2

The empirical rule states that approximately 68 percent of data falls within one standard deviation of the mean, 95 percent falls within two standard deviations, and more than 99 percent falls within three standard deviations.

Step-by-step explanation:

The empirical rule, also known as the 68-95-99.7 rule, states that for a bell-shaped distribution, approximately 68 percent of the data falls within one standard deviation of the mean, approximately 95 percent falls within two standard deviations, and more than 99 percent falls within three standard deviations.

In this case, with a mean of 20 and a standard deviation of 5:

1. The percentage of data within one standard deviation of the mean (15 to 25) would be approximately 68 percent.
2. The percentage of data within two standard deviations of the mean (10 to 30) would be approximately 95 percent.
3. The percentage of data within three standard deviations of the mean (5 to 35) would be more than 99 percent.