Certain app allows you to order from different types of cuisine. A driver for the food delivery app makes $6 for each order she delivers. Assume that deliveries occur randomly at a constant rate of 1.875 deliveries per hour, and different periods of time are independent of each other. Required:
a. A driver for the Food delivery app gets a bonus every time he accumulates 5 deliveries from an Asian restaurant. What is the expected number of deliveries he has to make to gain a bonus?
b. A driver for the Food delivery app gets a bonus every time he accumulates 5 deliveries from an Asian restaurant. What is the probability that he will have to make more than 25 deliveries to gain the bonus?
c. What is the probability that a driver for the delivery app does not visit a Mexican restaurant in 20 consecutive orders?
d. What is the probability that a driver for the delivery app visits an Asian restaurant at most 3 times in 20 consecutive orders?