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Customers arrive to a savings bank according to a Poisson distribution with mean 3 per hour....

Customers arrive to a savings bank according to a Poisson distribution with mean 3 per hour. Then, they either complete a transaction with a bank teller or meet with a financial officer, and leave the bank when they are done.

  1. What is the probability that exactly 2 customers arrive in the next three hours?
  2. What is the probability that at least 3 customers arrive in the next two hours?
  3. What is the probability that nobody arrives in the next 30 minutes?

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