Normal Distribution and Empirical Rule

What is the definition of a normal distribution?

• A normal distribution is a probability distribution that is symmetric and bell-shaped.

• A normal distribution is a probability distribution that is uniform and bell-shaped.

• A normal distribution is a probability distribution that is asymmetric and bell-shaped.

• A normal distribution is a probability distribution that is skewed and bell-shaped.

What are the characteristics of a normal distribution?

• A normal distribution has a standard deviation that determines the shape of the curve.

• A normal distribution has a mean, median, and mode that are all different.

• A normal distribution is characterized by a skewed, bell-shaped curve.

• A normal distribution is characterized by its symmetric, bell-shaped curve, with the mean, median, and mode being equal and located at the center. It has a standard deviation that determines the spread of the data, and the total area under the curve is equal to 1.

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

• 68%

• 90%

• 75%

• 50%

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

• 90%

• 80%

• 95%

• 99%

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

• 68%

• 99.7%

• 95%

• 90%

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Use the following information and the Empirical Rule to estimate the answer.

The ages of golfers are normally distributed, with a mean of 38 and a standard deviation of 4. Find the percentage of golfers that are between 30 and 46 years old. (Remember to draw a curve with the values to help you.)

• 68%

• 94%

• 95%

• 99.7%

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If this is the graph of data normally distributed with a mean of 30 and a standard deviation of 5, what label (number) is written at the blue circle?

• 20

• 15

• 40

• 30

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If this is the graph of data normally distributed with a mean of 30 and a standard deviation of 5, what label (number) is written at the blue circle?

• 20

• 15

• 40

• 30

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CCSS.HSS.ID.A.4

The mean life of a tire is 30,000 km. The standard deviation is 2000 km. Then, 68% of all tires will have a life between ___________ km and __________ km.

(Remember to draw a curve with the values to help you.)

• 28,000 km and 32,000 km.

• 24,000 km and 34,000 km.

• 26,000 km and 34,000 km.

• 27,000 km and 31,000 km.

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The shelf life of a particular dairy product is normally distributed with a mean of 12 days and a standard deviation of 3 days. About what percent of the products last between 12 and 15 days?

(Remember to draw a curve with the values to help you.)

• 68%

• 34%

• 16%

• 2.5%

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