A cafeteria serving line has a colfee um tram which customers serve themselves. Arrivals at the urn follow a Polsson cistribution at the rate of three per minute. In serving themselves, custormers take abcit 15 seconds, exponentially distributed a. How many customers would you expect to see; on average, at the cottee urn? b. How long would you expect it to take to git a cup of colfee? c. What percentage of time is the um being used? d. What is the probability that three or more people are in the cafeterla? Note: Do not round intermediate colculations. Round your answer to 1 decimal place. e. If the cafeteria instalis an automatic vendor that dispenses a cup of coffee at a constant time of 15 seconds, how many customers would you expect to see at the coffee un (wating and/or pouring coffee)? Note: Round your onswer to 2 decimal ploces. f. If the cafetella imstalls an automatic vendor that dispenses a cup of caffee at a constant time of 15 seconds, how long would you expect it to take (in minutes) to get a cup of colfee, including walting time? Note: Round your onswer to 2 decimol ploces. Round your answer to 2 decimal places