Scores on a test are approximately normally distributed with

Scores on a test are approximately normally distributed with a mean of 70 and a standard deviation of 9. The teacher wants to give A’s to the top 10% of students, B’s to the next 25%, and C’s to the next 42%. What is the bottom cutoff for a C grade? What is the bottom cutoff for a B grade? What is the bottom cutoff for an A grade?

Solution

a)
Bottom cutoof for \'C\' Grade = 10+25+42 = 77%
P ( Z > x ) = 0.77
Value of z to the cumulative probability of 0.77 from normal table is -0.74
P( x-u/ (s.d) > x - 70/9) = 0.77
That is, ( x - 70/9) = -0.74
--> x = -0.74 * 9+70 = 63.349  

b)
Bottom cutoof for \'B\' Grade = 10+25 = 35%

P ( Z > x ) = 0.35
Value of z to the cumulative probability of 0.35 from normal table is 0.39
P( x-u/ (s.d) > x - 70/9) = 0.35
That is, ( x - 70/9) = 0.39
--> x = 0.39 * 9+70 = 73.465  

c)
Bottom cutoof for \'A\' Grade = 10+25 = 10%
P ( Z > x ) = 0.1
Value of z to the cumulative probability of 0.1 from normal table is 1.28
P( x-u/ (s.d) > x - 70/9) = 0.1
That is, ( x - 70/9) = 1.28
--> x = 1.28 * 9+70 = 81.538