Normal Distribution Calculations

What is the area under the curve between z = 0 and z = 1.45?

• .9265

• .4265

• .4500

• .5000

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CCSS.HSS.ID.A.4

A dataset is normally distributed with a mean of 50 and a standard deviation of 5. What is the Z-score for a data point of 60?

• 1.5

• 2

• 2.5

• 3

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CCSS.HSS.ID.A.4

Using the Z-table, what is the probability of a Z-score being less than 1.5?

• 0.9332

• 0.8413

• 0.6915

• 0.7500

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CCSS.HSS.ID.A.4

According to the Empirical Rule, what percentage of data falls within one standard deviation of the mean in a normal distribution?

• 50%

• 68%

• 95%

• 99.7%

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CCSS.HSS.ID.A.4

A normal distribution has a mean of 100 and a standard deviation of 15. What is the probability of a randomly selected score being between 85 and 115?

• 68%

• 95%

• 99.7%

• 34%

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CCSS.HSS.ID.A.4

If a Z-score is -1, what is the probability of a data point being less than this Z-score?

• 0.1587

• 0.8413

• 0.5000

• 0.3085

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CCSS.HSS.ID.A.4

What is the Z-score for a data point that is 3 standard deviations above the mean?

• 1

• 2

• 3

• 0

Using the Empirical Rule, what percentage of data falls within three standard deviations of the mean?

• 68%

• 95%

• 99.7%

• 100%

Tags

CCSS.HSS.ID.A.4

A normal distribution has a mean of 70 and a standard deviation of 10. What is the Z-score for a data point of 50?

• -2

• -1

• 0

• 1

Tags

CCSS.HSS.ID.A.4

What is the probability of a Z-score being greater than 2.5?

• 0.0062

• 0.9938

• 0.0124

• 0.9876

Tags

CCSS.HSS.ID.A.4