Understanding Normal Distribution and the Empirical Rule

The video tutorial explains how to use the empirical rule to analyze a normally distributed set of exam scores with a mean of 74 and a standard deviation of 4. It covers calculating the percentage of scores within two standard deviations (66 to 82), scores less than or equal to the mean (50%), scores one standard deviation below the mean (16%), scores two standard deviations above the mean (97.5%), and scores one standard deviation above the mean (84%). The tutorial emphasizes the symmetry of the normal distribution curve and how it aids in these calculations.

What is the mean of the exam scores in the normal distribution discussed?

• 70

• 74

• 78

• 82

What is the standard deviation of the exam scores in the normal distribution?

• 8

• 6

• 4

• 2

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

• 50%

• 99.7%

• 95%

• 68%

What is the range of exam scores that approximately 95% of the data falls between?

• 74 and 78

• 62 and 86

• 66 and 82

• 70 and 78

What percentage of exam scores are less than or equal to the mean?

• 25%

• 50%

• 34%

• 68%

What percentage of exam scores are less than or equal to one standard deviation below the mean?

• 68%

• 50%

• 34%

• 16%

What percentage of exam scores are less than or equal to two standard deviations above the mean?

• 84%

• 95%

• 97.5%

• 99.7%

How much of the data falls between the mean and two standard deviations above the mean?

• 50%

• 13.5%

• 47.5%

• 34%

What percentage of exam scores are less than or equal to one standard deviation above the mean?

• 50%

• 95%

• 84%

• 68%

What is the percentage of exam scores between the mean and one standard deviation above the mean?

• 16%

• 34%

• 68%

• 50%