Question

A humanities professor assigns letter grades on a test according to the following scheme. A: Top 13% of scores B: Scores below the top 13% and above the bottom 60% C: Scores below the top 40% and above the bottom 23% D: Scores below the top 77% and above the bottom 8% F: Bottom 8% of scores Scores on the test are normally distributed with a mean of 70 and a standard deviation of 9.6. Find the minimum score required for an A grade. Round your answer to the nearest whole number, if necessary.

Answer 1

Solution :

mean = = 70

standard deviation = =9.6

Using standard normal table,

a ) P(Z < z) = 13%

P(Z < z) = 0.13

P(Z < -1.126) = 0.13

z =-1.126

Using z-score formula,

x = z * +

x = -1.126 * 9.6 +  70

= 59.19

Minimum score  = 59

b ) P(Z > z) = 40%

1 - P(Z < z) = 0.40

P(Z < z) = 1 - 0.40 = 0.60

P(Z < 0.2533) = 0.60

z = 0.2533

Using z-score formula,

x = z * +

x = 0.2533 * 9.6 + 70

= 72.43

Minimum score = 72

c ) P(Z < z) = 23%

P(Z < z) = 0.60

P(Z < -1.126) = 0.13

z =-1.126

Using z-score formula,

x = z * +

x = -1.126 * 9.6 +  70

= 59.19

Minimum score  = 59

d ) P(Z > z) = 8%

P(Z < z) = 0.08

P(Z < -1.405) = 0.08

z = -1.405

Using z-score formula,

x = z * +

x = -1.405 * 9.6 + 70

= 56.51

Minimum score = 52