A local childrens museum typically experiences more visits during summer. Assume that the number of adult tickets sold over summer are 20,000 and the number of children tickets sold are 35,000. Adult ticket prices are $20.00 and a childs ticket sells for $12.00. Each visitor to the museum spends on average $7.00 on food and beverage. The souvenir revenue is expected to be $120,000 over the summer season. The museum estimates a variable cost per visitor (adult or child) of $4 and a fixed cost of $600,000 over summer.

part A) Determine the profitability of the museum over the summer season.

part b) When solving part b, do not over-write part a. Now assume that the number of adult tickets sold are normally distributed with a mean of 20,000 and a standard deviation of 1500. Also assume that the number of children tickets sold is normally distributed with a mean of 35,000 and a standard deviation of 800. Run a simulation of 100 trials. What is the probability that the museums profit over summer is at least $480,000?