Empirical Rule and Normal Distributions Quiz

What percentage of data falls within one standard deviation of the mean in a normal distribution according to the empirical rule?

• 68%

• 95%

• 99.7%

• 50%

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CCSS.HSS.ID.A.4

If a set of test scores is normally distributed with a mean of 70 and a standard deviation of 10, what is the z-score for a test score of 90?

• 1

• 2

• 3

• 4

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CCSS.HSS.ID.A.4

Which of the following is NOT a characteristic of a normal distribution?

• Symmetry about the mean

• Mean, median, and mode are all equal

• Bell-shaped curve

• Skewed to the right

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CCSS.HSS.ID.A.4

CCSS.HSS.ID.A.3

According to the empirical rule, what percentage of data falls within two standard deviations of the mean in a normal distribution?

• 68%

• 95%

• 99.7%

• 50%

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CCSS.HSS.ID.A.4

CCSS.HSS.IC.B.4

Using the empirical rule, what percentage of data falls within three standard deviations of the mean in a normal distribution?

• 68%

• 95%

• 99.7%

• 50%

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CCSS.HSS.ID.A.4

If the mean of a normally distributed set of scores is 50 and the standard deviation is 5, what percentage of scores lies between 45 and 55?

• 68%

• 95%

• 99.7%

• 50%

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CCSS.HSS.ID.A.4

What is the z-score for a value that is exactly at the mean of a normal distribution?

• 0

• 1

• -1

• It cannot be determined without more information

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CCSS.HSS.ID.A.4

In a normal distribution, what percentage of the data lies below the mean?

• 25%

• 50%

• 75%

• 100%

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CCSS.HSS.ID.A.4

If a data set has a mean of 100 and a standard deviation of 20, what is the range of values that covers approximately 95% of the data according to the empirical rule?

• 60 to 140

• 80 to 120

• 90 to 110

• 40 to 160

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CCSS.HSS.ID.A.4

How do you calculate the z-score of a value in a data set?

• Subtract the mean from the value and divide by the standard deviation

• Divide the value by the mean

• Subtract the value from the mean and divide by the variance

• Add the mean to the value and divide by the standard deviation

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CCSS.HSS.ID.A.4