Discuss the below:
Task:
The new Lucky Lady Casino wants to increase revenue by providing buses that can transport gamblers from other cities. Research shows that these gamblers tend to be older, they tend to play slot machines only, and they have losses with a mean of $182 and a standard deviation of $105. The buses carry 35 gamblers per trip. The casino gives each bus passenger $50 worth of vouchers that can be converted to cash, so the casino needs to recover that cost in order to make a profit. Find the probability that if a bus is filled with 35 passengers, the mean amount lost by a passenger will exceed $50. Based on the result, does the casino gamble when it provides such buses?