Standard Deviation and Normal Distribution Quiz

What is the standard deviation of the following data set:

20, 13, 45, 83, 47, 25.

• 6

• 25.6

• 38.8

• 653.8

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CCSS.HSS.ID.A.2

CCSS.HSS.ID.A.4

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

Standard deviation tells us...

• the spread of the data

• the average of the data

• the range of the data

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CCSS.HSS.ID.A.2

CCSS.HSS.ID.A.3

When Avani goes bowling, her scores are normally distributed with a mean of 145 and a standard deviation of 12. Using the empirical rule, determine the interval that would represent the middle 68% of the scores of all the games that Avani bowls.

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CCSS.HSS.ID.A.4

When Julia goes bowling, her scores are normally distributed with a mean of 200 and a standard deviation of 14. Using the empirical rule, what percentage of the games that Julia bowls does she score between 158 and 242?

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CCSS.HSS.ID.A.4

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

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CCSS.HSS.ID.A.4

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

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CCSS.HSS.ID.A.2

CCSS.HSS.ID.A.4

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

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CCSS.HSA.CED.A.4

CCSS.HSA.REI.B.3

CCSS.HSS.ID.A.4

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

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CCSS.HSS.ID.A.4

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

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CCSS.HSS.ID.A.4

CCSS.HSS.MD.A.2