We are told that the data about the heights of men has a mean of 70 inches and a standard deviation of 2.5 inches. We are asked to find the percent of men that are within of one standard deviation of the mean height.
Let's find all the heights that are within one standard deviation (2.5 inches) of the mean (70 inches).
70 - 2.5≤Height≤70 + 2.5
⇕
67.5≤Height≤72.5
We found that the heights within one standard deviation of the mean are in the range from 67.5 inches to 72.5 inches. Let's highlight these heights on the bar graph.
Next, we can estimate the percentages represented by the highlighted bars. We will only give an example of an estimation, and your values may be a bit different.
Finally, we can find the percentage of men whose heights are within one standard deviation of the mean by adding the percentages.
Percent of men=11.5 %+13 %+ + 15.8 %+14.3 %+11.9 %≈ 67 %
We found that the percentage of men is about 67 %. Your answer might vary, depending on how you estimated the heights of the bars.
