Understanding the Empirical Rule

The video tutorial explains the empirical rule and its application to normal distributions, focusing on the heights of 16-year-old girls. It covers the characteristics of normal distributions, such as symmetry and the relationship between mean and standard deviation. The tutorial demonstrates how to calculate percentages of data within specific intervals using the empirical rule, providing multiple strategies for determining these percentages. It also explores how to find intervals containing certain percentages of the population.

What is the empirical rule used for in statistics?

• To determine the mean of a dataset

• To find the mode of a dataset

• To predict intervals and population percentages

• To calculate the median of a dataset

According to the empirical rule, what percentage of data lies within one standard deviation of the mean in a normal distribution?

• 50%

• 99.7%

• 95%

• 68%

What is a key characteristic of a dataset that can be modeled with a normal curve?

• It has multiple peaks

• It has many outliers

• It is skewed to the right

• It is single-peaked and symmetric

What is the mean height of 16-year-old girls in the U.S. according to the lesson?

• 62 inches

• 71 inches

• 65 inches

• 68 inches

What percentage of 16-year-old girls are between 62 and 68 inches tall?

• 34%

• 68%

• 95%

• 99.7%

How much of the data falls within three standard deviations of the mean in a normal distribution?

• 100%

• 99.7%

• 95%

• 68%

What percentage of 16-year-old girls are taller than 74 inches?

• 34%

• 13.5%

• 2.35%

• 0.15%

If a teenage boy is 59 inches tall, what percentage of 16-year-old girls are taller than him?

• 97.5%

• 95%

• 68%

• 50%

What is one strategy to determine the percentage of girls taller than a certain height?

• Count the number of girls taller than that height

• Use the empirical rule to find the area under the curve

• Calculate the mean height

• Estimate based on a sample

How can you find an interval that contains the height of 84% of 16-year-old girls?

• By using the mean height only

• By considering intervals within one standard deviation

• By using the median height

• By guessing based on experience