Suppose a “fair” die is rolled 100 times. Let $X_i$ be the value obtained in the i-th roll. Calculate an approximation for:
$P( \displaystyle\prod_{i=1}^{100} X_i \leq a^{100})$, where $1 < a < 6$
I know that $X_i$~Unif{1,2,3,4,5,6}, and I think I should use some kind of normal distribution to approximate the probability, but I don't know what to do with the product. Can someone help me?