Normal Distribution and Standard Deviation

Front

What is a normal distribution?

Back

A normal distribution is a probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean.

Front

What shape is another name for a normal distribution?

Back

Bell curve.

Front

What percentage of data falls within 1 standard deviation of the mean in a normal distribution?

Back

68%.

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CCSS.HSS.ID.A.4

Front

What percentage of data falls within 2 standard deviations of the mean in a normal distribution?

Back

95%.

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CCSS.HSS.ID.A.4

Front

What percentage of data falls within 3 standard deviations of the mean in a normal distribution?

Back

99.7%.

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CCSS.HSS.ID.A.4

Front

What is standard deviation?

Back

Standard deviation is a measure of the amount of variation or dispersion in a set of values.

Front

If the mean GPA of students is 3.2 with a standard deviation of 0.3, what is the range for 68% of students?

Back

Between 2.9 and 3.5.

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CCSS.HSS.ID.A.4

Front

What does it mean if data is 1 standard deviation from the mean?

Back

It means that the data point is within the range where approximately 68% of the data falls.

Front

In a normal distribution, what does the area under the curve represent?

Back

The area under the curve represents the total probability, which equals 1.

Front

What is the empirical rule?

Back

The empirical rule states that for a normal distribution, about 68% of the data falls within 1 standard deviation, 95% within 2 standard deviations, and 99.7% within 3 standard deviations.

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CCSS.HSS.ID.A.4