High School Math : Understanding Normal Distributions

Study concepts, example questions & explanations for High School Math

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Example Questions

Example Question #1 : Basic Statistics

Which of the following populations has a precisely normal distribution?

Possible Answers:

Correct answer:

Explanation:

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.

Example Question #2 : Basic Statistics

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

Possible Answers:

at least 40% of all values in the population

fewer than the number of values within one negative standard deviation of the mean

fewer than 20% of all values in the population

equal to the number of values within two negative standard deviations of the mean

equal to the number of values within one negative standard deviation of the mean

Correct answer:

equal to the number of values within one negative standard deviation of the mean

Explanation:

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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