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Given a normally distributed data set with the mean of 100 and the standard deviation of 15, according to the Empirical Rule, what percent of the data points are between 70 and 115?

A. 34%
B. 34%

Answer :

Final answer:

The Empirical Rule and standard deviations are used to estimate the percentage of data points between two values in a normally distributed data set.


Explanation:

The Empirical Rule, also known as the 68-95-99.7 rule, states that for a normally distributed data set, approximately 68% of the data falls within one standard deviation of the mean, 95% falls within two standard deviations, and 99.7% falls within three standard deviations.



In this case, the mean is -100 and the standard deviation is 15. To find the percent of data points between 7 and 115, we first need to find the number of standard deviations away these values are from the mean. For 7, we calculate (7 - (-100)) / 15 = 107 / 15 ≈ 7.13 standard deviations below the mean. For 115, we calculate (115 - (-100)) / 15 = 215 / 15 ≈ 14.33 standard deviations below the mean.



Since the data set is normally distributed, we can use the Empirical Rule to estimate the percentage of data points between 7 and 115. Since 7 is more than 3 standard deviations below the mean, we can assume that it falls within the 0.15% (0.15% * 2 = 0.30%) of data that is less than 3 standard deviations below the mean. Similarly, since 115 is less than 3 standard deviations below the mean, we can assume that it falls within the 0.30% (0.30% * 2 = 0.60%) of data that is less than 3 standard deviations below the mean. Therefore, the percent of data points between 7 and 115 is approximately 99.70% - 0.60% = 99.10%.


Learn more about Empirical Rule here:

https://brainly.com/question/30700783


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