4. Suppose that the inter-arrival time at a bus station has an exponential distribution with a mean of 20 minutes. Determine the following: (a) (10 points) The probability that 3 buses will arrive in the next hour. (b) (10 points) The probability that at least 4 buses will arrive in the next two hours. (c) (10 points) The probability that no bus will arrive in the next three hours. (d) (10 points) If no bus has arrived in the last two hours, what is the probability that at least one bus will arrive in the next 30 minutes?

3. A burger stall owner must make a single order for burgers. Each burger costs the owner $13 and leftover burgers are marked down to $5 for quick sale. Loss of goodwill from customers if burgers run out is $28.5 /burger. Estimated sales are given with the following probabilities: (a) (10 points) Determine the optimal order quantity. (b) (10 points) Determine the expected shortage and the expected surplus. (c) (10 points) Determine the total expected cost. 4. Suppose that the inter-arrival time at a bus station has an exponential distribution with a mean of 20 minutes. Determine the following: (a) (10 points) The probability that 3 buses will arrive in the next hour. (b) (10 points) The probability that at least 4 buses will arrive in the next two hours. (c) (10 points) The probability that no bus will arrive in the next three hours. (d) (10 points) If no bus has arrived in the last two hours, what is the probability that at least one bus will arrive in the next 30 minutes