Predicting Intervals and Population Percentages Using the Empirical Rule

This video tutorial explains how to use the Empirical Rule to predict intervals and population percentages in normally distributed data. It covers the characteristics of normal distributions, such as the bell curve shape and the relationship between the mean and standard deviation. The tutorial applies these concepts to the heights of 16-year-old girls, providing a detailed breakdown of height intervals. It also explores different strategies for calculating percentages and highlights multiple approaches to solving related problems.

What is the Empirical Rule used for?

• Predicting exact values in a data set

• Determining intervals and population percentages

• Identifying outliers in a data set

• Calculating the mean of a data set

Which of the following is a characteristic of a normal distribution?

• It has multiple peaks

• It is symmetric and single-peaked

• It is always skewed to the right

• The mean is always greater than the median

According to the Empirical Rule, what percentage of data lies within 1 standard deviation of the mean?

• 99.7%

• 50%

• 68%

• 95%

What percentage of 16-year-old girls are expected to be between 59 and 71 inches tall?

• 95%

• 68%

• 99.7%

• 47.5%

How much of the data falls outside 3 standard deviations from the mean?

• 13.5%

• 5%

• 2.35%

• 0.3%

If a boy is 59 inches tall, what percentage of girls are taller than him?

• 50%

• 34%

• 68%

• 97.5%

Which strategy can be used to find the interval containing 84% of the population?

• Using 3 standard deviations from the mean

• Using 1 standard deviation from the mean

• Using the median value

• Using 2 standard deviations from the mean