Question

A test is given and the average (μ_X) score was 190, with a SD (σ_X) of 50. Assuming a normal distribution for the grades, find the dividing line (test scores) between the A's, B's, C's, D's, and E's. The bottom 13% will be assigned the E's, the next 13% will be the D's, 50% will be the C's, the next 15% the B's and the top 9% will be the A's.

Answer 1

SOLUTION:

the given data as follows:

mean =

standard deviation =

we have to find the test scores, which devides the area as follows.

E = bottom 13%

D = next 13% area

C = next 50% area

B = next 15% area

A = next 9% area

so z score for (E) 0.13 area to the left = -1.13

the score which devide this area is

z score for D 0.26 (0.13+0.13) area to the left = -0.64

the score which devides this area

z score for D 0.76 (0.26 + 0.50) area to the left = 0.71

the score which devides this area

z score for D 0.91 (0.76+0.15) area to the left 1.34

the score which devides this area

so the graph which clearly shows all the separated region as follows