A survey of 50 lobster fishermen on Funafuti (an island in Tuvalu), found that they catch an average of 32 pounds of lobster per day with a standard deviation of four pounds.
a) If a fisherman is selected randomly, what is the probability that his catch is less than 20 pounds?
b) If a random sample of 30 lobster fishermen is selected, what is the probability that their average catch is one pound within the expected catch for a fisherman on Funafuti?