5 number from {1 to 70} will be selected at random and without replacement.

Use the Central Limit Theorem to approximate the theoretical probability that the sum of the five number 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 assumptions are and discuss how extreme (mild, moderate, severe) the violation is.