Question

the mean of the commute time to work for a resident of a certain city is 28.8 minutes. assume the standard deviation of the commute time is 8.1 minutes. what minimum percentage of the commuters in the city has a commute time within 2 standard deviations of the mean?

Answer 1

The minimum percentage of the commuters in the city has a commute time within 2 standard deviations of the mean is 75%.

Explanation:

We have no information about the shape of the distribution, so we use Chebyshev's Theorem to solve this question.

Chebyshev Theorem

At least 75% of the measures are within 2 standard deviations of the mean.

At least 89% of the measures are within 3 standard deviations of the mean.

An in general terms, the percentage of measures within k standard deviations of the mean is given by
`100(1 - (1)/(k^(2)))`.

Applying the Theorem

The minimum percentage of the commuters in the city has a commute time within 2 standard deviations of the mean is 75%.