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 64 and standard deviation of 14. 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 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

From a standard normal table, a right tail area of 0.15 corresponds to a z- value of 1.04, a right tail area of 0.4 corresponds to a z-value of 0.25, a right tail area of 0.7 corresponds to a z-value of - 0.52, a right tail area of 0.95 corresponds to a z-vue of - 1.64

We know that z = (x-mean) /standard deviation

So, x = z x standard deviation + mean

We have, z = 1..04; x= 1.04x14+64=78.56, this is cutoff for A grade.

Z= 0.25, x = 0.25x14+64=67.5 cutoff for B grade

z=-0.52, x=-0.52x14+64=56.72 cutoff for C grade

z=-1.64, x= - 1.64x14+64=41.04 cutoff for D grade

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