Question

Suppose that your statistics professor tells you that the scores on a midterm exam were approximately normally distributed with a mean of 74 and a standard deviation of 7. The top 15% of all scores have been designated A's. Your score is 87. Did you receive an A

Answer 1

Yes, you have received an A

Explanation:

Mean grade (μ) = 74

Standard deviation (σ) = 7

The top 15% have to score at least at the 85th percentile of the normal distribution. The 85th percentile has a corresponding z-score of z =1.04.

The minimum grade X, that qualifies as an A is given by:

`z=(X-\mu)/(\sigma)\\1.04=(X-74)/(7) \\X=81.28`

Since the requirement for an A is getting a grade higher than 81.28, and you got a score of 87, then you have received an A.