Question

An instructor gives a 100 point exam which grades are normal distributed. the mean is 66 and the standard deviation is 8. If there are 12% A, 10% B, 60% C, 10% D, and %8 F. find the scores and then divide the distribution into those categories.

Suppose 50 students were selected from a class who took the exam in the above problem. What is the probability the class average was a 65 and a 67?

Answer 1

An instructor gives a 100 point exam which grades are normal distributed. the mean is 66 and the standard deviation is 8. If there are 12% A, 10% B, 60% C, 10% D, and %8 F. find the scores and then divide the distribution into those categories.

z value for bottom 8% = -1.405, x = 66-1.405*8 =54.76

z value for bottom 18% = -0.915, x = 66-0.915*8 =58.68

z value for bottom 78% = 0.772, x = 66+0.772*8 =72.176

z value for bottom 88% = 1.175, x = 66+1.175*8 =75.4

The categories are:

less than 54.76 = F

54.76-58.68 = D

58.68-72.176 = C

72.126-75.4 = B

Above 75.4 = A

Suppose 50 students were selected from a class who took the exam in the above problem. What is the probability the class average was a 65 and a 67?

Standard error = sd/sqrt(n) = 8/sqrt(50) = 1.1314

Z value for 65, z =(65-66)/1.1314 = -0.88

Z value for 67, z =(67-66)/1.1314 = 0.88

P( 65< meanx <67) = P( -0.88<z<0.88)= P( z <0.88) – P( z < -0.88)

=0.8106-0.1894

=0.6212