I'm trying to solve the following exercise:
A teacher in probability knows that the qualification of a student in his final exam is a random variable $X$ with $E[X]=75$.
a) Find a superior upper bound for the probability of the student be greater than $85$.
b) If the professor knows that the variance is $25$, what can you say about the probability of a student get a qualification between $65$ and $85$?
c) How many students have to do the exam in such way that, with probability at least $0.9$, the average of the ratings will be $75$ in less than $5$?
For a) I find a upper bound with Markov's inequality.
For b) I use Chebyshev inequality:
$$P(|X-E(X)|\geq\epsilon)\leq\frac{Var(X)}{\epsilon^2}.$$
But for c) I don't know how to start. Can anyone give me a hint?
Thanks for the help.