The Professor's Response

Professor,

Could you solve step by step the following problem:

A small computing center has found that number of jobs submitted per day to its computers has a distribution that is approximately mound-shaped and symmetric. with a mean of 68 jobs and a standard deviation of 8. Where do we expect approximately 95% of the distribution to fall?

See the professor's answer below.

Hi Maria,

This problem gives us information that leads us to assume the data is bell shaped, "approximately mound-shaped and symmetric." As a result, this problem can be done using the empirical rule (especially since it only asks for an approximate answer).

The empirical rule tells us that approx. two standard deviations will capture 95% of the data, so we need to add 2 standard deviations to the mean and take 2 standard deviations from the mean to create our interval.

(mean - 2SD, mean + 2SD) = (68 - 2*8, 68 + 2*8) = (68 - 16, 68 + 16) = (52, 84).

I hope that helps,

Professor McGuckian