Estimating Percentages using the Empirical Rule

This video tutorial explains how to estimate the percentage of a population within a certain range using the empirical rule. It covers the characteristics of a normal distribution, the concept of standard deviation, and how to apply the empirical rule to calculate data ranges. The empirical rule, also known as the 68-95-99.7 rule, is used to determine the percentage of data within one, two, and three standard deviations from the mean. The tutorial uses the example of adult American female heights to illustrate these concepts.

What is a key characteristic of a normal distribution?

• It is skewed to the right.

• It has a symmetric bell-shaped curve.

• It is always uniform.

• It has multiple peaks.

What does standard deviation measure in a dataset?

• The highest value in the dataset.

• The spread of data around the mean.

• The total number of data points.

• The average value of the data.

What is another name for the empirical rule?

• The 50-75-90 rule.

• The 68-95-99.7 rule.

• The 60-80-100 rule.

• The 70-85-95 rule.

Before applying the empirical rule, what must be verified about the data?

• It is uniformly distributed.

• It is approximately normally distributed.

• It is skewed to the left.

• It has a mean of zero.

According to the empirical rule, what percentage of data falls within two standard deviations of the mean?

• 95%

• 68%

• 99.7%

• 50%

What is the range of heights for 95% of adult American females according to the empirical rule?

• 65 to 75 inches

• 57.5 to 72.5 inches

• 60 to 70 inches

• 62.5 to 67.5 inches

What percentage of data falls within three standard deviations of the mean in a normal distribution?

• 100%

• 95%

• 68%

• 99.7%