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 71 and standard deviation of 12. The top 15% of the class will get an A, the next 25% 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

(b) The B cutoff is a grade of  
(c) The C cutoff is a gr

(d) The D cutoff is a grade of

Explanation / Answer

standard normal distribution (Z) is

Z = (X - mu)/sigma

mu = maen = 71% and sigma = standard deviation = 12% so the transformation is

Z = (X - 71)/12

The teacher wants 15% of the students to receive A's. From a table for the standard normal distribution, 15% of the area lies above 1.05. Thus the grade that separates the A's from the B's is the number X that satisfies

1.05 = (X - 71)/12

That is X = 83.6

The next 25% of the students are to receive B's. From the normal table 25% of the area lies above 0.67. Thus

0.67 = (X - 71)/12

and thus X = 79.04

The next 30% of the students are to receive C's. From the normal table 30% of the area lies above 0.52. Thus

0.52 = (X - 71)/12

and thus X = 77.24

The next 25% of the students are to receive D's. From the normal table 25% of the area lies above 0.67. Thus

0.67 = (X - 71)/12

and thus X = 79.04

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