# 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.

May 25, 2018

$23.7$ minutes to $35.7$ minutes

#### Explanation:

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 $6$ to the mean to find the limits of those observations:
$29.7 - 6 = 23.7$
$29.7 + 6 = 35.7$

Therefore, the limit of the observations where 68% of the times fall is $23.7$ minutes to $35.7$ minutes .

Hope this helps!