A cafeteria serving line has a coffee urn from which customers serve themselves. Arrivals at the urn follow a Poisson distribution at the rate of 2.5 per minute. In serving themselves, customers take about 18 seconds, exponentially distributed.

b. How long would you expect it to take to get a cup of coffee? (Round your answer to 2 decimal places.)

d. What is the probability that three or more people are in the cafeteria? (Do not round intermediate calculations. Round your answer to 1 decimal place.)

e. If the cafeteria installs an automatic vendor that dispenses a cup of coffee at a constant time of 18 seconds, how many customers would you expect to see at the coffee urn (waiting and/or pouring coffee)? (Do not round intermediate calculations. Round your answer to 2 decimal places.)

f. If the cafeteria installs an automatic vendor that dispenses a cup of coffee at a constant time of 18 seconds, how long would you expect it to take (in minutes) to get a cup of coffee, including waiting time? (Do not round intermediate calculations. Round your answer to 2 decimal places.)