Your movie theatre has 100 seats. Customers buy tickets randomly, at an average rate of 3 customers per day, and sales begin 30 days before the performance. In the interests of fairness, you offer each customer a random price, normally distributed with a mean of $15 and a standard deviation of $3. Once a customer buys a ticket, there is a 10% chance they won't show up because they're busy that day.

1. What is the probability I'll make more than $1,000 for a given performance?

2. Suppose I sell 110 tickets (i.e., oversell my theatre). What is the probability someone won't get a seat on the day of the performance?

3. My staff is busy, and can only handle the sale of 8 tickets per day. If I want to ensure that there is a 95% probability I can handle all sales, do I need to hire more staff?