Exploring the 68-95-99.7 Rule

The video tutorial explains standard deviation and the 68-95-99.7 rule using ACT scores as an example. It covers how to label a normal distribution curve, calculate scores at different standard deviations, and apply the rule to determine the percentage of students scoring within certain ranges. The tutorial emphasizes the importance of understanding these concepts for analyzing normally distributed data.

What was the mean ACT score in 2010?

• 27

• 21

• 24

• 18

What does the standard deviation measure in a dataset?

• The lowest value in the dataset

• The highest value in the dataset

• The spread of the data points from the mean

• The average value of the data points

If the mean ACT score is 21 and the standard deviation is 5.2, what is the score one standard deviation above the mean?

• 31.4

• 26.2

• 21

• 15.8

What is the score two standard deviations below the mean if the mean is 21 and the standard deviation is 5.2?

• 31.4

• 15.8

• 10.6

• 26.2

Which ACT scores are one standard deviation away from the mean?

• 10.6 and 31.4

• 15.8 and 26.2

• 5.4 and 36.6

• 21 and 26.2

According to the 68-95-99.7 rule, what percentage of data falls within one standard deviation of the mean?

• 100%

• 99.7%

• 68%

• 95%

What percentage of students scored between 15.8 and 26.2 on the ACT?

• 100%

• 95%

• 99.7%

• 68%

What percentage of students scored below 10.6 on the ACT?

• 13.5%

• 2.5%

• 2.35%

• 0.15%

How much percentage is in each section within one standard deviation of the mean?

• 34%

• 0.15%

• 13.5%

• 2.35%

What is the percentage of students within three standard deviations of the mean?

• 100%

• 99.7%

• 68%

• 95%