Question

A set of data is normally distributed with a mean of 327 and a standard deviation of 27.

What percentage of the data is below 357?
Enter your answer as a number rounded to the nearest tenth, like this: 42.5

Answer 1

86.7%

Explanation:

For questions regarding values related to a normal distribution, a suitable calculator is required. Numerous calculators, apps, web sites, and spreadsheets are capable of answering this question.

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One standard deviation above the mean is 327 +27 = 354, so the value is expected to be slightly more than 50% +34% = 84%. It is no surprise, then, that a calculator tells you 86.7% of the data is below 857.

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Additional comment

The "empirical rule" tells you 68% of the area is within 1 standard deviation of the mean. The distribution is symmetrical, so half that, 34%, is between the mean and 1 standard deviation above the mean. Of course, 50% of the data is below the mean.