1. In a game, you have found a reward with 15 treasure boxes. From experience you know that 1 in 5 treasure boxes contain rare items.

a) You want to know the probability of finding 4 rare items here. Can the normal approximation to the binomial distribution be used? Justify your answer and describe why it is important to check that the normal approximation can be used

b) You want to know the probability of finding 8 treasure chests with magic items. Can the normal approximation to the binomial be used?

c) Calculate the probability that you find 8 treasure boxes with rare items in a collection of 50 chest, using the normal approximation to the binomial distribution.