We have a mean of 126 and standard deviation of 18. Use the 68-95-99.7 rule to determine the percent of scores in the data set expected to be between the scores 72 and 144. Give your answer in decimal

Answer 1

Begin by observing that 126-72 = 54, and 54/18 = 3. So 72 is three standard deviations below the mean.

The 68-95-99.7 rule tells us that 99.7% of the data is within three standard deviations of the mean. But we are only looking at three standard deviations below the mean, so we use 1/2 of 99.7% = 49.85%. In other words, 49.85^ of the scores are between 72 and 126.

In a similar fashion, we observe that 144-126 = 18 so 144 is one standard deviation above the mean. We know that 68% of the data will be within one standard deviation of the mean in both directions, but we are only looking at one direction so we take half: 68/2=34, so 34% of the data will be between 126 and 144.

We can add those two percentages together: 49.85% + 34% = 83.85%.

So 83.85% of the data will be between 72 and 144.