The Professor's Response

I was doing the sample exam for Chapter 1 and 2 and for question 6 I wasn't sure how you were able to get 34% for each side to know that the answer was 68% total?

See the professor's answer below.

Hi Diasha,

The empirical rule states that for a bell-shaped distribution an interval that spans one standard deviation below the mean to one standard deviation above the mean will capture a total of 68% of the data. The bell curve is symmetric which means that its left half is a perfect mirror image of its right half. Because of this symmetry, the 68% is evenly split into 34% on the left and 34% on the right. The symmetry of the bell curve is what makes this possible.

We could not do the same if we were working with Chebyshev's theorem. There is no assumption of symmetry when using Chebyshev's theorem.

I hope that clears it up,

Professor McGuckian