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
when you simplify this you get 1/16x^8
A. 485 is %3 of 500, but the deviation sets it slightly lower than that
See attachment for one such shell. The volume is given by the sum of infinitely many thin shells like this, each with radius
and height determined by the vertical distance between the upper blue curve and the lower orange curve for any given
, i.e.
.
The volume is then
