Question

For 200 students taking a common chemistry final, the mean score was 85.2 and the standard deviation was 3.1. If these scores have a normal distribution, what range would be expected to include about 68 percent of the scores?

Answer 1

Standard normal model in statistics:

• About 68% of values fall within one standard deviation of the mean.(mean 1 x Standard deviation)
• About 95% of the values fall within two standard deviations from the mean. (mean 2 x Standard deviation)
• Almost all of the values — about 99.7% — fall within three standard deviations from the mean.(mean 3x Standard deviation)

These facts are what is called the 68 95 99.7 rule, sometimes called the Empirical Rule.

Going by the above rule,

The expected range to include 68 percent of the scores is : Mean - 1 x standard deviation, Mean + 1x standard deviation

Given,

Mean score = 85.2

Standard deviation = 3.1

Mean - 1 x standard deviation = 85.2 - 1 x 3.1 = 85.2 - 3.1 = 82.1

Mean + 1 x standard deviation = 85.2 + 1 x 3.1 = 85.2 + 3.1 = 88.3

Therefore, The expected range to include 68 percent of the scores is (82.1, 88.3)