A teacher wishes to \"curve\" a test whose grades were normally distributed with

Question

A teacher wishes to "curve" a test whose grades were normally distributed with a mean of 63 and standard deviation of 13. The top 10% of the class will get an A, the next 30% of the class will get a B, the next 30% of the class will get a C, the next 25% of the class will get a D and the bottom 5% of the class will get an F. Find the cutoff for each of these grades. (Round your answers to two decimal places.)

(a) The A cutoff is a grade of _________

(b) The B cutoff is a grade of ________

(c) The C cutoff is a grade of ______

(d) The D cutoff is a grade of ______

Explanation / Answer

Z = (X - mean)/standard deviation

a) P(Z < (X - 63)/13) = 1 - 0.1

P(Z < (X - 63)/13) = 0.9

(X - 63)/13 = 1.28

X = 79.64

The A cutoff is a grade of 79.64

b) P(Z < (X - 63)/13) = 0.6

(X - 63)/13 = 0.25

X = 66.25

The B cutoff is a grade of 66.25

c) P(Z < (X - 63)/13) = 0.3

(X - 63)/13 = -0.52

X = 56.24

The C cutoff is a grade of 56.24

d) P(Z < (X - 63)/13) = 0.05

(X - 63)/13 = -1.645

X = 41.62

The D cutoff is a grade of 41.62

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