Question

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.

Answer 1

`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!