Extending the Empirical Rule: Finding Percentages within a Normal Distribution

This video tutorial explains how to use the empirical rule to find percentages of a population within certain intervals. It reviews the characteristics of a normal distribution and demonstrates how to extend the empirical rule beyond the standard 68%, 95%, and 99.7% intervals. The tutorial includes examples using adult American female heights to illustrate the application of the empirical rule and provides tips for effectively extending the rule.

What is a key characteristic of a normal distribution?

• It has no standard deviation.

• The mean is always at the far left.

• It is a symmetric bell-shaped curve.

• It is always skewed to the right.

According to the empirical rule, what percentage of data falls within one standard deviation of the mean?

• 50%

• 68%

• 95%

• 99.7%

How can the empirical rule be extended beyond the standard percentages?

• By using only the 68%, 95%, and 99.7% values.

• By applying it to derive other percentages.

• By ignoring the rule entirely.

• By using a different mean value.

What is the mean height of adult American females used in the example?

• 60 inches

• 65 inches

• 70 inches

• 75 inches

What percentage of adult American females are estimated to be taller than 5 feet 10 inches?

• 2.5%

• 10%

• 5%

• 1%

What is a helpful tip when extending the empirical rule?

• Ignore the symmetry of the distribution.

• Use only the mean value.

• Always use a skewed distribution.

• Visualize the normal curve and shade areas.

What percentage of females are between 60 inches and 67.5 inches tall according to the example?

• 99.7%

• 68%

• 81.5%

• 95%