Qtaestion 12 (5 poles) 50 asteners arme at a tenerwetw a bank ding a shour perbd
ID: 365926 • Letter: Q
Question
Qtaestion 12 (5 poles) 50 asteners arme at a tenerwetw a bank ding a shour perbd, ten re anal rate 250 astres per hour O10 customers per hour O tive customers per hour 50cuarners per hour Question 13 (S polnts Lel us oonslder that customers amve al the rate of seven per hour and wait for an average 0.25 hour In a shop. Using Littie's law, delermine the average number of cuslomers in the queuing system O 2 O 24 1.25 O 1.75 Question 14 (S polnts) suppose an mem stays in an inventory system for an average of days, and the demand rate for tem ls 15 unts per day. Determine the average Inventory level for this tem O 100 0 80 O 120 O 150 Question 15 (10 polnts) Assume the average amrval rate at a servibe center is tive customers per hour. Determine the probability of three customers arriving in any random hour o 4% 05% 10% 14%Explanation / Answer
Question 12
Given Data,
Number of customers arrived = 50
Duration of 50 customer arrival= 5 Hour
Arrival Rate = Number of Customers Arrived/ Time Duration
=50/5=10
Therefore, Arrival Rate =10 per hour
Question 13
Given Data,
Arrival Rate of Customers = 7 per hour
Waiting time W= 0.25 hour
According to Little’s Law, Average number of customers in the queue L = W = 7*0.25 =1.75
Therefore, the average number of customers in the queue is L=1.75 or approximately 2.
Question 14
Demand rate of the unit = 15 units per day
Waiting time W is 8 days
According to Little’s Law, the average inventory level L = W = 15*8=120 units.
Therefore, the average inventory level is L=120 units
Question 15
Given data, Average arrival rate of customers = 5 per hour
The expected arrival rate n = 3 per hour
T = 1 hour
Applying Poisson distribution, the probability is,
P(n,t)= ((t)ne- t )/n!
=(5*1)3e(-5*1)/3!
==(5)3e(-5)/(3*2*1)
=(125*0.000674)/6
=0.8422/6
=0.1403
=14%
The Probability