Question

Problem 10-19

At a border inspection station, vehicles arrive at the rate of 15 per hour in a Poisson distribution. For simplicity in this problem, assume that there is only one lane and one inspector, who can inspect vehicles at the rate of 16 per hour in an exponentially distributed fashion.

Return to ques c. What is the utilization of the inspector? (Round your answer to 1 decimal place.) 13 points Answer is complete and correct. Utilization 93.8 % d. What is the probability that when you arrive there will be three or more vehicles ahead of you? (Round your answer to 1 decimal place.) Answer is complete but not entirely correct. Probability 0.8%

Answer 1

The utilisation of the inspector and the probability that when you arrive there is 3 or more vehicles ahead of you is also found out. All the calculations and results are given in the following image :

utilization factor, p=5 where Arrival rate, s= 15/hour Scovice rate, M = 161 hour 3o, utilization of Inspector 15 20.9375 20.98=93-8% Probability of having 'n' Customers in the system, - Pn=6*(1-0).h=0), 2, 3, . . . . . s - where, <) Prob. that there is 3 or more customers ahead- Prob- that there is 4 or more customer in the system- given there is 1 or more than one customer in the System. - ie; P (234/b = P(nah. P (n=1) Plne) - - Pn34) ( PLAIR =P (AJOP(13) plnz PC3) Pln24 = t[ Plu=o) + P(6-1) + P(n=2) A 212=3) = 0.7725 Plu217= 1- [P(n=o] P(n=1) = 0 (1-0) = 0.0586 = 0.9375 So, P (524/2 ) = 0.7725 - 0.824 0.9375 82-4 % customes- So Probability that there is three or more ahed =0.824 or 82.4%

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