Customers arrive to a bank teller according to a Poisson process with a mean rate of 10/hr. Forty percent of the customers need to make a bank deposit only. Fifty percent need to make a withdrawal. The rest of the customers need special assistance from a bank consultant. The bank is open to the public between 9:00 AM and 5:00 PM.

a. What is the probability that the next customer will only make a deposit?
b. What is the probability that the next withdrawal-only customer will will arrive within 5 minutes?
c. What is the expected number of bank-consultant-seekers customers that will arrive during the 8-hr workday?
d. What is the probability of exactly 10 customers arriving between 12:00 PM and 1:00 PM?
e. What is the probability exactly of four deposit-only customers arriving, four withdrawal-only customers, and two bank-consultant-seeker customers between 12:00 PM and 1:00 PM?