The mean a person gets to work is 29.7 minutes. If the standard deviation is 6 minutes, within what limits would you expect approx 68% of the times to fall? Assume the distribution is approx bell shaped.
A bell shaped distribution means that it follows the empirical (or sigma) rule, where:
68% of the observations fall within 1 standard deviation of the mean
95% of the observations fall within 2 standard deviations of the mean
99.7% of the observations fall within 3 standard deviations of the mean.
It's also shown here on a graph:
Since we know that the standard deviation is 6 minutes, and we want to know where 68% (or one standard deviation) of the observations fall, we can subtract and add
Therefore, the limit of the observations where 68% of the times fall is
Hope this helps!