There are a number of probability claims made in the Lottery tips. In this problem, verify whether these claims are true. Consider the current rules (5/70 + 1/25) of the CA MEGA millions game.

(a) Consider the High-Low Lotto Tip. Find the exact probability that the five white numbers selected will all be high (that is within [36,70]).

(b)Consider the Sum Lotto Tip. Use the Central Limit Theorem to approximate the theoretical probability that the sum of the five white balls will fall between 132 and 223 (both inclusive).

Discuss the appropriateness of using the Central Limit Theorem in this case. If any of the assumptions of the theorem are violated, state what these assumtions are and discuss how extreme (mild, moderate, severe) the violation is.

Note: You are supposed to calculate a theoretical probability. You are NOT being asked to use past lottery data to estimate this probability.