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 is the area under the standard normal curve?

Back

The total area under the standard normal curve is equal to 1.

Front

What does a Z-score represent in a normal distribution?

Back

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

Front

What is the empirical rule in statistics?

Back

The empirical rule states that for a normal distribution, approximately 68% of the data falls within one standard deviation of the mean, 95% within two standard deviations, and 99.7% within three standard deviations.

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CCSS.HSS.ID.A.4

Front

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

Back

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

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CCSS.HSS.ID.A.4

Front

What is the area to the right of Z=0 in a standard normal distribution?

Back

The area to the right of Z=0 is 0.5, as it represents half of the total area under the curve.

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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 in a normal distribution.

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CCSS.HSS.ID.A.4

Front

What is the significance of the shaded region in a normal distribution graph?

Back

The shaded region in a normal distribution graph represents the probability of a certain range of values occurring.

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CCSS.HSS.ID.A.4

Front

How do you interpret a Z-score of 1.5?

Back

A Z-score of 1.5 indicates that the data point is 1.5 standard deviations above the mean.

Front

What is the area under the curve between Z=-1 and Z=1?

Back

The area under the curve between Z=-1 and Z=1 is approximately 68%.

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CCSS.HSS.ID.A.4