Philatelists (stamp collectors) often buy stamps at or near retail prices, but, when they sell, the price is considerably lower. For example, depending on the mix of a collection, condition, demand, economic conditions, etc., a collection may sell at x% of the retail price, where x is normally distributed with a mean equal to 45% and a standard deviation of 4.5%. If a philatelist has a collection to sell that has a retail value of $30,000, what is the probability that the philatelist receives these amounts for the collection?
a. More than $15,000
b. Less than $15,000
c. Less than $12,000