Assume that you run a call center that receives an average of 3 calls per minute with a Poisson distribution. Use this information to answer questions 1 to 4.
-----------------------------------------------------------------------------------------------------------
Ans:
average number of calls=3 calls per minute
P(x=k)=exp(-3)*(3^k/k!)
1)
P(x=2)=exp(-3)*(3^2/2!)=0.2240
2)
P(x=4)=exp(-3)*(3^4/4!)=0.1680
Now,
average number of calls in 20 sec=(3/60)*20=1
P(x=k)=exp(-1)*(1^k/k!)
3)
P(x=1)=exp(-1)*(1^1/1!)=0.3679
4)
P(x>=2)=1-P(x<=1)
=1-P(x=0)-P(x=1)
=1-exp(-1)*(1^0/0!)-exp(-1)*(1^1/1!)
=1-exp(-1)-exp(-1)
=0.2642
Assume that you run a call center that receives an average of 3 calls per minute...
A call center receives an average of 13 calls per hour. Assuming the number of calls received follows the Poisson distribution, determine the probability would receive exactly 15 calls. Round to four decimals.
A call center receives an average of 18 calls per hour. Assuming the number of calls received follows the Poisson distribution, determine the probability would receive exactly 11 calls. Make sure that your answer is between 0 and 1.
4. The emergency telephone (911) center in a large city receives an average of 210 calls per hour during a typical day. On average, each call requires about 121 seconds fora dispatcher to receive the emergency call, determine the nature and location of the problem, and send the required individuals (police, firefighters, or ambulance) to the scene. The center is currently staffed by 7 dispatchers a shift but must have an adequate number of dispatchers on duty and it has...
A customer service center in Gary, Indiana receives, on average, 2.5 telephone calls per minute. If the distribution of calls is Poisson, what is the probability of receiving more than 4 calls during a particular minute? Do not round intermediate calculations. Round your final answer to four decimals. Format for probabilities: 0.0000
A customer support center for a computer manufacturer receives an average of 2.7 phone calls every five minutes. Assume the number of calls received follows the Poisson distribution. a. What is the probability that no calls will arrive during the next five minutes? b. What is the probability that 3 or more calls will arrive during the next five minutes? c. What is the probability that 3 calls will arrive during the next ten minutes? d. What is the probability...
to a call center where an automated machine can answer three calls in a five-minute period. Assume that calls occur at an average rate of 1.2 every five minutes. [Hint: Poisson Distribution A. Calculate the probability that no calls will occur during the next five minutes? B. Caleulate the probability that more calls (more than the system can handle) will occur during the next 5 minutes? (Hint: think of the complement!]
Exercise 2.3 The time between phone calls to a call center is exponentially distributed with mean 60 seconds. (a) What is the probability that exactly 4 calls arrive in the next 2 minutes? (6) What is the probability that at least 2 calls arrive in the next 2 minutes? (c) What is the probability that no buses arrive in the next 2 minutes? (d) Given that a call has just arrived, what is the probability that the next call arrives...
Calls arrive at a call center at the rate of 30 per hour. What is the probability that the next call arrives in a. less than 4 minutes? b. more than 9 minutes? c. less than 1 minute? 1. a. The probability that the next call arrives in less than 4 minutes is (Round to four decimal places as needed.)
6. Service calls come to a maintenance center are 3 per minute on the average. Find the probability that no more than 4 calls come in a given minute: b. between 3 to 10 calls come in a given minute: more than 10 calls come in a 4-minute period. a. с.
3. A customer support center for Bell Computer Company (BMC) receives an average of 2.5 phone calls every 5 minutes. Assume that the number of calls received follows Poisson distribution with λ = 2.5 in answering the following questions What is the probability that no calls will arrive during the next five minutes? What is the probability that 5 calls will arrive during the next 5 minutes? What is the probability that at least 3 calls will arrive during the...