Based on a true story! In Costa Rica, there are howling monkeys living in mango trees. People sometimes annoy them and they will throw mangoes at the people. Five tourists arrive in a car and start harassing the monkeys. The monkeys attack the tourists by throwing mangoes. Assume each attack on a tourist is independent, and that in every attempt there is a 0.15 chance that the monkey will hit a tourist.
a) Show that the number of tourists hit follows a binomial distribution.
b) Find probability that they hit 2 tourists.
c) Find the expected number of tourists hit in the attack.
d) Find the standard deviation of the number of tourist hit.
e) Find the probability of hitting more than one, but no more than four tourists.