High School

According to the empirical rule, if the data form a "bell-shaped" normal distribution, what percent of the observations will be contained within 3 standard deviations around the arithmetic mean?

A. 68.26
B. 75.00
C. 95.0
D. 99.7

Answer :

Final answer:

The empirical rule states that in a 'bell-shaped' or normal distribution, 99.7% of observations fall within 3 standard deviations of the mean.

Explanation:

According to the empirical rule in statistics, which applies to a normal distribution — also known as a 'bell-shaped' distribution — about 99.7% of the observations are contained within 3 standard deviations around the arithmetic mean. This means that if you were to plot the data on a graph, almost all the data points (99.7%) would fall within the area that is between 3 standard deviations below and 3 standard deviations above the mean.

To further explain, the empirical rule gives us the following information: about 68% of data fall within one standard deviation of the mean, 95% within two standard deviations, and 99.7% within three standard deviations. This rule is particularly useful in statistics for predicting where values are likely to fall within the data set.

Learn more about Empirical Rule here:

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Answer:99.7

Step-by-step explanation: