consider grading an exam on curve where it is decided ahead

consider grading an exam on curve where it is decided ahead of time that a certain percentage of the class will earn A\'s, a certain percentage B\'s, and so on. Suppose the exam scores for a large chemistry class are normally distributed with a mean of 68 and a standard deviation of 14. if the top 10% of the scores are given a grade A, what is the minimum score required to earn an A?

Solution

minimum score to get an A

so you have to be in the top 10 % i.e. >90th percentile

and in the normal distribution with mean zero and std 1

0.9 is achieved at 1.28

so in the N(68,14)

it will be at 68 + 14*1.28 = 85.92

So roughly minimum marks required = 86