Question

A professor at a local community college noted that the grades of his students were normally distributed with a mean of 74 and a standard deviation of 10. the professor has informed us that 6.3 percent of his students received a's while only 2.5 percent of his students failed the course and received f's. if 5 students received f's, how many total students were there in the class?

Answer 1

We are interested in the left-end area under the standard normal curve that has the area 0.025.  

But the problem seems to be simpler than that:

If n = number of students in the class, and we know that 2.5% of these students failed the course, and that 5 failed, then we can surmise that

0.025n = 5.  Solving for n by multiplying both sides by 40, we get n = 200.

There were 200 students in the class.

It is perfectly fair for a teacher to put more info into a problem statement than you really need to solve the problem.  That seems to be what happened here.