Question

The mean grade in this class last semester was 78.3, and the variance was 34.6 . The distribution of grades was unimodal and symmetrical.. determine how many students are likely to fail the class (<60), and how many students are likely to get a “A” (>90), if 60 students are enrolled. Show all your work, and provide a sentence explaining each step of your calculations.

Answer 1

"Unimodal and symmetrical" = normal

Z = (score-mean)/SD

variance = SD^2

Find table in the back of your statistics text labeled something like "areas under normal distribution" to find the proportions/probabilities related to the Z scores. Multiply by 60.

Answer 2

So would I do this? 60-78.3/5.882 and 90-78.3/5.882
and multiply my answer by 60?

meaning I am multiplying the z-score by 60 to find the percentage/probabitlity?