Standard Deviation and Variance Empirical Rule

On a standardized test, Cathy had a score of 74, which was exactly 1 standard deviation below the mean. If the standard deviation for the test is 6, what is the mean score for the test?

• 68

• 71

• 77

• 80

On a standardized test, a score of 82 falls exactly 1 standard deviation below the mean. If the standard deviation for the test is 4, what is the mean score for the test?

• 78

• 80

• 84

• 86

On a standardized test, Phillip scored 84, exactly 1 standard deviation above the mean. If the standard deviation for the test is 6, what is the mean score for the tes?

• 72

• 78

• 84

• 90

On a standardized test, a score of 86 falls exactly 1.5 standard deviations below the mean. If the standard deviation for the test is 2, what is the mean score for the test?

• 83

• 84.5

• 87.5

• 89

On a standardized test, Laura received a score of 85, which was exactly 2 standard deviations above the mean. If the standard deviation for the test is 4, what is the mean for the test?

• 93

• 87

• 83

• 77

In the diagram, the shaded area represents approximately 95% of the scores on a standardized test. If these scores range from 78 to 92, which could be the standard deviation?

• 3.5

• 7.0

• 14.0

• 20.0

In the diagram, about 68% of the scores fall within the shaded area, which is symmetric about the mean. The distribution is normal and scores in the area range from 50 to 80. What is the standard deviation of the scores in this distribution?

• 7.5

• 15

• 30

• 65

The heights of a group of girls are normally distributed with a mean of 66 inches. If 95% of the heights of these girls are between 63 and 69 inches, what is the standard deviation of the group?

• 1

• 1.5

• 3

• 6

In a normal distribution, 68% of the scores fall between 72 and 86 and the mean is 79. What is the standard deviation?

• 3.5

• 7

• 10.5

• 14

On a test that has a normal distribution of scores, a score of 57 falls 1 standard deviation below the mean, and a score of 81 is 2 standard deviations above the mean. Determine the mean score of this test.

• 57

• 65

• 73

• 81