Question

On a statistics test for a class of 40 students, the grades were normally distributed.The mean grade was 74, and the standard deviation was 8.

2. Janis scored 76 on this test.

A. What was her z-score for this grade

b. What percent of the class scored lower than Janis?

c. Approximately how many students in the class scored lower than Janis?

3. The minumum passing grade on this test was 70. Approximately how many students scored lower than 70 on this test.

4. To receive an “A” on this test, a minimum grade was required. How many students scored above 90?

5 Ronnie’s grade was the 85th percentile, P85, for this test.

A. This means that_____ percent of students in the class scored lower than ronnie, and ___ percent of students scored higher than Ronnie.

b. What was roonie’s grade on this test.

Answer 1

µ = 74

sd = 8

2) z = (X - µ) / sd

a) Z = (76 - 74) / 8 = 0.25

b) P(Z < 0.25) = 0.5987 = 59.87%

c) Number of students in the class scored lower than Janis = 40 * 0.5987 = 24

3)

                             

                             = P(Z < -0.5)

                              = 0.3085

Number of students scored lower than 70 on this test = 40 * 0.3085 = 12

4)

                             

                              = P(Z > 1.75)

                              = 1 - P(Z < 1.75)

                              = 1 - 0.9599

                              = 0.0401

Number of students scored above 90 = 40 * 0.0401 = 2

5) a) This means that__85___ percent of students in the class scored lower than ronnie, and _15__ percent of students scored higher than Ronnie.

b) Z for 85 percentile = Z_0.85 = 1.04

roonie’s grade on this test = 76 + 1.04 * 8 = 84.32 or 84