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The are effective as far as the domain of the random variable, and that domain may be infinite.

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Q: What is the effective range of standard deviation units on both sides of the mean?
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What percentage of the data falls outside 1 standard deviation of the mean?

One standard deviation for one side will be 34% of data. So within 1 std. dev. to both sides will be 68% (approximately) .the data falls outside 1 standard deviation of the mean will be 1.00 - 0.68 = 0.32 (32 %)


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What percent of a normal population is within 2 standard deviations of the mean?

By the definition of standard deviation, 95.46% of the normal population will be within 2 SD of the mean. Explanation: The normal distribution of a population means it follows the "bell curve". The center of this bell curve is the population's mean value. One standard deviation defines two areas (on the left and right side of the central "mean" value) under the bell curve that each have 34.13% of the population. The next standard deviation adds two additional areas under the curve, each having 13.6% of the population. Adding the areas under the curves on both sides gives us (34.13% + 13.6%) x 2 = 95.46%


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How many sides are these on a standard pencil?

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