Understanding Normal Distributions - High School Math

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Question

Which of the following populations has a precisely normal distribution?

Answer

A normal distribution is one in which the values are evenly distributed both above and below the mean. A population has a precisely normal distribution if the mean, mode, and median are all equal. For the population of 3,4,5,5,5,6,7, the mean, mode, and median are all 5.

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Question

If a population has a normal distribution, the number of values within one positive standard deviation of the mean will be . . .

Answer

In a normal distribution, the number of values within one positive standard deviation of the mean is equal to the number of values within one negative standard deviation of the mean. The reason for this is that the values below the population mean exactly parallel the values above the mean.

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