Answer to Question #323858 in Statistics and Probability for Bless

Question

 48000 fair dice are rolled independently. Let X count the number of sixes that appear.

(a) What type of random variable is X?

(b) Write the expression for the probability that between 7500 and 8500 sixes show.

(c) The sum you wrote in part (b) is ridiculous to evaluate. Instead, approximate the value by a normal distribution and evaluate in terms of the distribution Φ(x) = P(N(0,1) ≤ x) of a standard normal random variable.

(d) Why do you think a normal distribution is a good choice for approximation?