Exploring Normal Distribution and the Empirical Rule

The video tutorial explains the concept of normal distribution, focusing on how data is spread in relation to the mean. It covers the 68-95-99.7 rule, which describes the percentage of data within one, two, and three standard deviations from the mean. The tutorial also provides a practical example using dollar values to demonstrate how to calculate data ranges using standard deviation.

What does the normal distribution primarily describe?

• Variation of data from the median

• Spread of data around the mean

• Bimodal distribution of data

• Skewness of data towards the mode

How much data falls within one standard deviation from the mean in a normal distribution?

• 34%

• 68%

• 95%

• 99.7%

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CCSS.HSS.ID.A.4

What percentage of data is found within two standard deviations from the mean?

• 68%

• 99.7%

• 95%

• 100%

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CCSS.HSS.ID.A.4

How much data lies within three standard deviations from the mean?

• 68%

• 95%

• 99.7%

• 100%

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CCSS.HSS.ID.A.4

What is the percentage of data points that are extremely rare, falling outside three standard deviations?

• 13.5%

• 5%

• 2.35%

• 0.3%

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CCSS.HSS.ID.A.4

If the mean is $34 and the standard deviation is $5.20, what is the value one standard deviation above the mean?

• $49.60

• $28.80

• $44.40

• $39.20

Calculate the value two standard deviations below the mean if the mean is $34 and each standard deviation is $5.20.

• $13.60

• $18.40

• $28.80

• $23.60

What is the value three standard deviations above the mean if the standard deviation is $5.20?

• $59.00

• $44.40

• $49.60

• $54.80

Between which two values does 95% of the data lie if the mean is $34?

• $13.60 and $54.80

• $23.60 and $44.40

• $18.40 and $49.60

• $28.80 and $39.20

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CCSS.HSS.ID.A.4

What is the range of values within one standard deviation from the mean in this normal distribution?

• $34.00 to $44.40

• $23.60 to $44.40

• $18.40 to $49.60

• $28.80 to $39.20