Answer to Question #290576 in Statistics and Probability for manche

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

Let X be a random variable represents the score of a randomly selected student, then X~$N(70, 8^2)$

The point is to find such value a that $P(X>a)=0.1$

$P(X>a)=0.1\implies P(N(70,8^2)>a)=0.1\implies P(70+8N(0,1)>a)=0.1\implies P(N(0,1)>{\frac {a-70} 8})=0.1\implies {\frac {a-70} 8}=1.28\implies a=80.24$

So, if teacher put a = 81, then amount of students receiving A-grade will be no more than 10%