Interpreting Normal Distributions

Interpreting Normal Distributions

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The topic this week is Interpreting Normal Distributions.  Interpretation depends on understanding of the 3-Sigma Rule:

The 3-Sigma Rule

In statistics, the 68-95-99.7 rule — or three-sigma rule, or empirical rule — states that for a normal distribution, nearly all values lie within 3 standard deviations of the mean. More accurately, 68.27%, 95.45% and 99.73% of the values lie within one, two and three standard deviations of the mean.

Assume that a population is normally distributed with a mean of 100 and a standard deviation of 15. Would it be unusual for the mean of a sample of 3 to be 115 or more? Why or why not?

This rule should give you a basis for determining if it would be unusual for “the mean of a sample of 3 to be 115 or more” for the population stated.

Here is a website that might help you frame your response:

https://www.mathsisfun.com/data/standard-normal-distribution.html