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NotSoSmart  May 17, 2018
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The empirical rule (sometimes referred to as 68-95-99.7% rule) will come be handy here. This empirical rule expresses the percent of the values that are 1 to 3 standard deviations in both directions of the mean with a normal distribution:

 

Source: https://i2.wp.com/www.statistics-made-easy.com/wp-content/uploads/2016/08/empirical-rule.png?w=382&ssl=1

 

As the problem mentions, the standard deviation here is 4, and mean is 64. Therefore, one standard deviation in both directions would yield 60 and 68. The problem wants to know the percentage of values that fall in this range. As you can tell from the image above, 68% of data falls in this range. 

 

Note: The empirical rule can only be utilized in very specific circumstances. It just so happened that I could use it here. If a data value is 1.5 standard deviations away, then other methods would have to be used. 

 
TheXSquaredFactor  May 18, 2018

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