the class average on a statistics exam is 80 with a standard deviation of 4 points. what is the percentage of students who scored 68 and 82 on the exam?

Answer 1

I am guessing you distribution of exam grades is normally distributed and you probably meant "what is the percentage of students who scored between 68 and 82 on the exam?" If my assumptions are correct then lets

1) find the percentage of students who scored less than 82 (we will call this value z2)

2) find the percentage of students who scored less than 68 (we will call this z1)

3) We will subtract z1 from z2 to get those who scored between 68 and 82

Let X be the random variable that represents the score on a stats exam then we convert each X to a standard normal random variable Z by the transformation (X-mean)/(standard deviation) = Z

1) Prob( X < 82 ) = Pr ( Z < (82-80)/4) = Pr(Z<.5) = φ(.5) = z2 = .69146

2) Prob( X < 68 ) = Pr (Z < (68-80)/4) = Pr(Z<-3) = φ(-3) = z1 = .00135

3) Now z2 - z1 = .69146 - .00135 = .69011

The percentage of students who score between 82 and 68 is .69011 ≈ 69% . That is my final answer.