Shakari M.

asked • 05/19/15

what proportion of a normal distribution is within one standard deviation of the mean

how do i figure out what proportion of a normal distribution is within one standard deviation of the mean

1 Expert Answer

By:

David W.

tutor
“Rules of thumb” are wonderfully useful in lots of fields of study, especially math.  Many of the formulas and rules that you learn in early math, you will derive in later math classes.

The 68-95-99.7 rule is such a rule.  It allows you to calculate percentage (proportion) of the normal frequency distribution that is within 1, 2,or 3 standard deviations.  Later, in calculus, you can take the rather complicated formula for the normal curve and calculate the area under (what’s called integrate) it to determine what percentage of the total area (or percent of the observations in the population) are within that range.

Just as an observation (pun intended), proportions of the normal distribution are very likely (also a probability and statistics term) to be represented as a percent (here, 68%).
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05/19/15

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