Question

13. A professor determined that the grades on the Statistic Final are normally distributed with a mean grade of 68 and a standard deviation of 15

            a)   If Mohammed had a z score of 1.25, what was his grade?

2. Students in the top 12 % receive an A the student what is the lowest grade a student can get and still get an A?
3. Students in the bottom 15% will fail the course. What is the cutoff grade a student can get and still pass?

Answer 1

13)

Given that,

mean = = 68

standard deviation = = 15

z = 1.25

Using z-score formula,

x = z * +

x = 1.25 * 15 + 68 = 86.75

Grade = 86.75

(b)

P(Z < 1.175) = 0.88

z = 1.175

x = 1.175 * 15 + 68 = 86.625

Lowest grade = 86.625

(c)

P(Z < -1.04) = 0.15

z = -1.04

x = -1.04 * 15 + 68 = 52.4

Cutoff = 52.4