Answer to Question #330847 in Statistics and Probability for sarr

Question

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?

Answer 1

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