Question

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 asked a consultant to determine a proper level of staffing. The consultant assumes that the calls come at random over time, so that the Poisson probabilities apply How many calls should the emergency call center expect in a 20-minute period? Please show how you arrived at your answer. a. 2 points Define X to be the number of telephone calls to the emergency call center ina 20-minute period and assume that X has a Poisson Probability distribution. Please calculate the probability that the call center will receive 70 calls in the 20- minute period. b. c. Please calculate the probability that the call center will receive at most 80 calls d. Please calculate the probability that the call center will receive fewer than 55 e. Please calculate the probability that the call center will receive at least 65 calls f. Please calculate the probability that the call center will receive more than 70 g. Calculate and interpret the standard deviation of X. in the 20-minute period. Show your work. calls in the 20-minute period. Show your work. in the 20-minute period. Show your work. calls in the 20-minute period. Show your work. [2 points] 2 points 2 points 2 points) 2 points] 12 points For what purpose can the emergency call center use the kind of information you have calculated above? If the call center wants to limit the mean caller waiting time to less than 2 seconds, do you think they should add an eighth dispatcher to each shift? Please show how you arrived at your answer. [Note: the caller waiting time in this problem is the time between the emergency telephone starts ringing and the time a dispatcher picks it up.] h. 3 points

Answer 1

3 E(メ\ リP(x1 10-10 e れ ん20min.2 80) e午 了? ' Scanned with CamScanner