# statistics

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The time to complete a standardized exam is approximately normal with a mean of 70 minutes and a standard deviation of 10 minutes. Using the 68-95-99.7 rule, if students are given 90 minutes to complete the exam, what percentage of students will not finish?

• statistics -

Here is what they mean by that rule:

68% finish within one std. deviation.
95% finish within two std. deviations (50 to 90 minutes in this case).
99.7% finish withing three std. deviations.

Considering the second group, half (47.5%) will finish within 70 to 90 minutes. Since the fraction above the mean is 50% for a normal distribution, that means 2.5% will not finish at all in 90 minutes.
A more exact value, using a calculator, is 2.3%

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