Certain app allows you to order from different types of cuisine. According with the app's records 27% of the orders are to an American food restaurant, 40% to an Asian food restaurant, 15% to a Mexican food restaurant, 8% to a Dessert place, and the rest are to other types of food. Assume that incoming orders are independent of each othe. Required:
a. A driver for the Food delivery app gets a bonus every time he accumulates 5 deliveries from a Mexican restaurant. What is the probability that he will have to make more than 25 deliveries to gain the bonus?
b. What is the probability that a driver for the delivery app does not visit a Dessert restaurant in 20 consecutive orders?
c. What is the probability that a driver for the delivery app visits a Mexican restaurant at most 3 times in 20 consecutive orders?
d. A driver for the Food delivery app makes $6 for each order she delivers. Assume that deliveries occur randomly at a constant rate of 2.5 deliveries per hour, and different periods of time are independent. What is the probability that she will make more than $75 in a four-hour shift?