A random variable is normally distributed with a mathematical expectation of $5$ and a variance of $9$. Find the probability that the arithmetic mean of $9$ values of this random variable is $>5.5$.
I have no idea how this can be solved, I would be very happy if you could help.
Hint: A linear function of (independent) normal RVs has normal distribution. Find the expectation and the variance of the arithmetic mean, then you just look at the probability tables.