Exploring the Normal Distribution and the 68-95-99.7 Rule

This video tutorial covers the concept of normal distribution, explaining its characteristics and significance in data analysis. It distinguishes between parameters and statistics, using symbols like x-bar, mu, and sigma to represent sample and population data. The tutorial introduces the 68-95-99.7 rule, which helps approximate areas under the normal curve, and provides practice questions to reinforce understanding.

What symbol is used to represent the sample mean?

• Sigma

• mu

• x-bar

• s

What does the Greek letter mu (μ) represent in a normal distribution?

• Population standard deviation

• Sample standard deviation

• Population mean

• Sample mean

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CCSS.HSS.ID.A.4

Which shape is commonly associated with the normal distribution?

• Square

• Bell-shaped

• Circular

• Linear

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CCSS.6.SP.A.3

What happens to the normal distribution curve when the mean increases?

• No change

• Shifts left

• Shifts right

• Becomes flatter

If the standard deviation is decreased, what happens to the height of the normal distribution curve?

• It gets taller

• It gets shorter

• It shifts left

• It shifts right

According to the 68-95-99.7 rule, what percentage of data falls within one standard deviation of the mean?

• 95%

• 68%

• 99.7%

• 50%

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CCSS.HSS.ID.A.4

What is the approximate percentage of data that falls between two standard deviations from the mean?

• 68%

• 95%

• 85%

• 99.7%

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CCSS.HSS.ID.A.4

What percentage of the population is between four and seven feet tall according to the 68-95-99.7 rule?

• 85%

• 99.7%

• 68%

• 95%

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CCSS.HSS.ID.A.4

In the practice question, what is the area contained between 70 and 90?

• 47.5%

• 95%

• 99.7%

• 68%

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CCSS.HSS.ID.A.4

What is the total area contained between -2 and 1 in the normal distribution example?

• 68%

• 81.5%

• 99.7%

• 95%

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CCSS.HSS.ID.A.4