Question

The final marks for the Wednesday class in Business Statistics are ready to be posted. The class average is 80%, with a standard deviation of 6 . Use the Empirical Rule to answer the following questions. (Round the final answers to 2 decimal places.) a. What percentage of the grades are above 62? b. What percentage of the grades are below 68 ? c. What percentage of the grades are less than 68 or more than 86 ?

Answer 1

Approximately 32% of the grades are above 62, approximately 16% of the grades are below 68, and approximately 48% of the grades are either below 68 or above 86.

Step-by-step explanation:

To answer the questions using the Empirical Rule, we can use the percentages mentioned in the rule. For a bell-shaped distribution, approximately 68% of the data falls within one standard deviation of the mean, approximately 95% falls within two standard deviations, and more than 99% falls within three standard deviations.

a. To find the percentage of grades above 62, we need to find the percentage of grades that fall more than one standard deviation below the mean. Since the class average is 80% and the standard deviation is 6, one standard deviation below the mean is 80 - 6 = 74. Therefore, approximately 32% of the grades are above 62.

b. To find the percentage of grades below 68, we need to find the percentage of grades that fall more than one standard deviation above the mean. Since the class average is 80% and the standard deviation is 6, one standard deviation above the mean is 80 + 6 = 86. Therefore, approximately 16% of the grades are below 68.

c. To find the percentage of grades that are less than 68 or more than 86, we can add the percentages from part a and part b. Approximately 32% + 16% = 48% of the grades fall either below 68 or above 86.