Areas Under the Standard Normal Curve

Front

What is the standard normal distribution?

Back

The standard normal distribution is a normal distribution with a mean of 0 and a standard deviation of 1.

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CCSS.HSS.ID.A.4

Front

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

Back

Approximately 68% of the data falls within one standard deviation of the mean.

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CCSS.HSS.ID.A.4

Front

What percentage of data falls within two standard deviations of the mean in a normal distribution?

Back

Approximately 95% of the data falls within two standard deviations of the mean.

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CCSS.HSS.ID.A.4

Front

What percentage of data falls within three standard deviations of the mean in a normal distribution?

Back

Approximately 99.7% of the data falls within three standard deviations of the mean.

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CCSS.HSS.ID.A.4

Front

What is the area under the standard normal curve to the left of z = 0?

Back

The area is 0.5 or 50%.

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CCSS.HSS.ID.A.4

Front

What does a z-score represent?

Back

A z-score represents the number of standard deviations a data point is from the mean.

Front

How do you find the area under the normal curve between two z-scores?

Back

You can find the area by looking up the z-scores in the standard normal distribution table and subtracting the smaller area from the larger area.

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CCSS.HSS.ID.A.4

Front

What is the area under the normal curve between z = -1.96 and z = 1.96?

Back

Approximately 0.95 or 95%.

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CCSS.HSS.ID.A.4

Front

What is the significance of the area under the curve in a normal distribution?

Back

The area under the curve represents the probability of a random variable falling within a certain range.

Front

What is the area under the normal curve to the right of z = 1.28?

Back

Approximately 0.1003 or 10.03%.

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CCSS.HSS.ID.A.4