Standard Deviation and Distribution

The shelf life of a particular dairy product is normally distributed with a mean of 12 days and a standard deviation of 3 days.

About what percent of the products last between 12 and 15 days?

• 68%

• 34%

• 16%

• 2.5%

What is the standard deviation of the following data set: 20, 13, 45, 83, 47, 25.

• 6

• 25.6

• 38.8

• 653.8

The picture shows the formula for standard deviation. What does x̄ represent in the formula.

• the number of items in the data set

• standard deviation

• summation (add all the numbers together)

• the average of the data set

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

• 3.5

• 7

• 14

• 20

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

• 7.5

• 15

• 30

• 65

In a normal distribution, x + 2σ = 80 and x − 2σ = 40 when x represents the mean and σ represents the standard deviation. The standard deviation is...

• 10

• 20

• 30

• 60

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 for this group?

• 1

• 1.5

• 3

• 6

On a test that has a normal distribution, a score of 17 falls two standard deviations below the mean, and a score of 32 falls one standard deviation above the mean. Determine the mean of this test.

• 27

• 15

• 37

• 5

One thousand students took a test resulting in a normal distribution of the scores with a mean of 80 and a standard deviation of 5. Approximately how many students scored between 75 and 85?

• 950

• 815

• 680

• 475

On a standardized exam, the scores are normally distributed with a mean of 250 and a standard deviation of 50. Find the z-score of a person who scored 375 on the exam.

• 1

• 1.5

• 2

• 2.5