The Decatur Fire Department makes annual door to-door solicitations for funds. Residents of each visited house are asked to contribute $15 (and receive a free family portrait package), $25 (and receive two free family portrait packages), or $35 (and receive three free family portrait packages). An analysis from previous years’ solicitations indicates that the following:
• Only 80% of the homes visited have someone at home.
• When someone is at home, there is only a 40% chance that he or she will make a donation.
• Of the people making donations, there is a 50% chance they will contribute $15, a 25% chance they will contribute $25, and a 15% chance they will contribute $35. Occasionally (10% chance), a person makes a donation in excess of $35. Such distributions follow a discrete uniform distribution between $40 and $50 (in increments of $1).
The fire chief plans to visit 30 houses tomorrow. Set up a simulation model and replicate it N times to determine the probability that the chief will receive more than $300 in donations from these 30 houses.