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.


The answer is 24. Recall normal distribution graph. 


*

*Around 68% of data is between standard deviation -1 to 1. Here it is between 20(24-1x4) to 28(24+1x4).

*Around 96% of data is between standard deviation -2 to 2. Here it is between 16(24-2x4) to 32(24+2x4).

*Around 100% of data is between standard deviation -3 to 3. Here it is between 12(24-3x4) to 36(24+3x4).


Range = Maximum number - Minimum number = 36-12 = 24
