In a community bank on average 5 customers arrive in each ho

In a community bank, on average 5 customers arrive in each hour. Suppose that the arrival times between one customer and the next one are independent exponential random variables with the same parameter .

(a) Find the value of . How many minutes do you expect to wait on average between the arrivals of one customer and the next one?

(b) What is the probability that during an hour no customer arrives?

(c) What is the probability that during an hour three or more customers arrive?

(d) What is the probability that there are more than 30 minutes between the arrivals of the 2nd and 3rd customer of the day?

(e) What is the probability that three customers will arrive within 20 minutes?

(f) How many minutes do you expect to wait until the 12th customer arrives?

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