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Answer:
A) 1.79
b) 71%
c) 0.75 minutes
d) 0.537 minutes
e) 0.343, 0.240 , 0.1681
Explanation:
L = average number of customers in the system ( 200 / 80 ) = 2.5
a = poission distribution per hour = 200
b = service rate of cashier = 280
A) average number of moviegoers waiting in line to purchase ticket
Lq = L - = 2.5 - (200/280) = 2.5 - 0.71 = 1.79
B) percentage of cashier been busy
p = a/b = 0.71 = 71%
C) average time spent by a customer in the system
w = L / a = 2.5 / 200 = 0.0125 hours = 0.75 minutes
D) average time spent waiting in line to get to the ticket window ?
W2 = Lq / a = 1.79 / 200 = 0.00895 hours = 0.537 minutes
E) probabilities of people in the system
i) more than two people
p ( x ≥ 2 ) = 1 - ( p0 + p1 + p2 ) = 1 - 0.657 = 0.343
more than three people
ii) p ( x ≥ 3 ) = 1 - (p0 + p1 + p2 + p3 ) = 1 - 0.7599 = 0.240
iii) more than four people
p ( x ≥ 4 ) = 1 - ( p0 - p1 + p2 + p3 + p4 ) = 1 - 0.8319 = 0.1681