On a recent Summative Assessment, the mean score for the Algebra 1 class was 72 and the standard deviation was 7. See the normal distribution curve below that represents the data and answer the following questions. If 30 students took the quiz, how many are within 7 points of the mean?

Reasoning:

The empirical rule says that about 68% of the population is within 1 standard deviation of the mean. This applies to the normal distribution.

The mean in this case is 72 and the standard deviation is 7.

One standard deviation below the mean is 72-7 = 65, while one standard deviation above the center point is 72+7 = 79. This is visually shown as the closest tickmarks to the center 72. Each tickmark represents a unit of standard deviation (eg: 85 is two standard deviations above the mean, since it's 2 tickmarks above 72).

Saying "within 7 points of the mean" therefore is the same as saying "the score is between 65 and 79, inclusive of both endpoints".

So you're teacher is asking how many students got between 65 and 79. As mentioned at the very top, roughly 68% of the population fits this description.

Meaning,

68% of 30 = 0.68*30 = 20.4 = 20 students got a quiz score within seven points of the mean.

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