Question #330847

The scores for a mathematics course seem to be normally distributed with mean 70 & standard deviation of 8. If the instructor wishes to give an A grade to 10% of the students, what should be the dividing line between an A grade and a B grade?


1
Expert's answer
2022-04-20T02:13:10-0400

Suppose that XX is a random variable that corresponds to the score for a mathematics. Then, P(Xa)=0.1P(X\geq a)=0.1. aa corresponds to the dividing line between AA and BB. We have: P(Xa)=a+f(x)dxP(X\geq a)=\int_{a}^{+\infty}f(x)dx, where f(x)=182πe(12(x708)2)f(x)=\frac{1}{8\sqrt{2\pi}}e^{(-\frac12\left(\frac{x-70}{8}\right)^2)}. For a=80.25a=80.25 we get: P(Xa)0.100053P(X\geq a)\approx0.100053. Thus, 80.2580.25 is as a dividing line. (The answer is rounded up to two decimal places).


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