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 does the area under the normal curve represent?

Back

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

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CCSS.HSS.ID.A.4

Front

What percent 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 percent 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 percent 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 Z-score?

Back

The Z-score is a statistical measurement that describes a value's relationship to the mean of a group of values, expressed in terms of standard deviations.

Front

How do you find the area to the left of a Z-score?

Back

To find the area to the left of a Z-score, you can use a Z-table or a calculator that provides cumulative probabilities.

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CCSS.HSS.ID.A.4

Front

What is the area to the left of Z = 0?

Back

The area to the left of Z = 0 is 0.5 or 50% of the total area under the curve.

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CCSS.HSS.ID.A.4

Front

What is the area to the left of Z = -2.37?

Back

The area to the left of Z = -2.37 is approximately 0.0089.

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CCSS.HSS.ID.A.4

Front

What is the area to the left of Z = -2.04?

Back

The area to the left of Z = -2.04 is approximately 0.0207.

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CCSS.HSS.ID.A.4