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percentage within a given amount of standard deviations

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For the normal distribtion, the mean plus and minus 1.96 standard deviation will include what percent of the observations?
What is the formula to calculate the percentage?

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Helpfull illustrations included as attachments. A complete solution along with detailed explanation.

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Hi there,

I will attempt to give a full explanation to this problem.

You likely know that the normal, or bell curve, is "big in the middle and small at the ends." The area beneath the curve is directly related to the "percent of observations." The bigger the area, the bigger the percentage. Please note that the total area beneath the curve is 1. The x-axis is centered at the mean and the notches on the x-axis represent the standard devations. The ...

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