7. A bank has three tellers with expected service times of 15 minutes, 10 minutes, and 5 minutes. The service times have an exponential distribution. Assume that immediately after a teller completes service, the next person in line begins getting served by that teller. (a) There is no queue, and each teller has been busy with a customer for 5 minutes when Sharon enters the bank. What is the expected amount of time until Sharon leaves the bank? (b) Suppose that in the previous question, Talia arrives immediately after Sharon (while Sharon is still in the queue). Talia gets in line behind Sharon. What is the expected amount of time until Talia leaves the bank? (c) Suppose that customers arrive to the bank according to a Poisson process with rate 12 per hour. If all three tellers are busy, what is the probability that a customer arrives to the bank before any of the tellers finish serving their current customer?

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