The marks in an examination for a physics paper have normal distribution with mean μ and variance σ2 . 10% of the students obtain more than 75 marks and 20% of them obtained less than 40 marks. find the value of μ and σ

Let be the random variable for the number of marks a given student receives on the exam.

10% of students obtain more than 75 marks, so

where follows a standard normal distribution. The critical value for an upper-tail probability of 10% is

where denotes the CDF of , and denotes the inverse CDF. We have

Similarly, because 20% of students obtain less than 40 marks, we have

so that

Then are such that

and we find