How to estimate the range of a normal distribution when the mean and standard deviation are given For example, how would you respond to this question?

The earnings of one-hundred workers in a company are normally distributed. If the mean of this data set is 24 and the standard deviation is 4, find an approximate value for the range.


Recall that about $99.7\%$ of data under a normal curve falls within three standard deviations of the mean. When you are given the mean and standard deviation, this seems like a pretty good way to approximate the range. So since the mean is $24$, we could estimate that most of the data falls in the interval $$[24-3(4), \;24+3(4)] \;=\; [12,36].$$ So the range is $36-12 = 24$.
