The scores are adjusted so that the mean score is about mu =75 and the standard deviation sigma =5. What percent of the scores fall between 65 and 75?

Answer 1

Compute Z₁ equal to (65 - 75)/5 or -2. A Table Of Proportions Of Area Under The Standard Normal Curve will give a percentage decimal of |-0.4772| for Z = -2 which translates to 47.72%.

Compute Z₂ equal to (75 - 75)/5 or 0. A Table Of Proportions Of Area Under The Standard Normal Curve will give a percentage decimal of 0.0000 for Z = 0 which translates to 0%.

It then follows that (47.72 - 0)% or 47.72% of the scores fall between 65 and 75.