During the morning hours at a catalog sales department, telephone calls come in

Question

During the morning hours at a catalog sales department, telephone calls come in at the rate (Poisson) of 47 per hour Calls that cannot be answered immediately are put on hold. The system can handle 10 callers on hold. If additional calls come in, they receive a busy signal. The 3 customer service representatives who answer the calls spend an average of 3 minutes with a customer. Use Table 1 and Table 2. a What is the probability that a caller will get a busy signal? (Hint: Solve for log Kor In K using trial and error.) (Do not round intermediate calculations. Round your answer to 5 decimal places.) Probability b. What is the probability that a customer will be put on hold? (Do not round intermediate calculations. Round your answer to 3 decimal places.) Probability

Explanation / Answer

= 47

There are three customer service representative who spend an average 3 minutes with a customer of serve 20 customers per hour

Therefore Service rate µ = 60

=

Caller will get a busy signal when there is already 10 callers in queue which means 11 caller in the system

P11 = 11(1- ) = 0.01476

Customer will be put on hold when there is atleast one customer in the system

P = 1 – P0­ = = 0.783

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