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Law Incorporation [45]
1 year ago
14

Students returning to a secondary school have to pass through a check point at the rate of 50 per though. The average time for c

hecking is 35 seconds. The arrival rate and service rate follow a Poisson distribution. There is a delay and the principal is willing to include another check point to reduce the average time of checking to 28 seconds if the idle time is less than 10% and the average queue length is more than 10 students, check whether the introduction of an extra check point is justifiable.
Mathematics
2 answers:
zysi [14]1 year ago
8 0

The average queue length is greater than 10 students, the introduction of an extra checkpoint is justifiable.

<h3>How to explain the information?</h3>

Since the arrival rate and service rate follow a Poisson distribution, we can use the Poisson arrival rate formula to calculate the average queue length.

Average queue length = (arrival rate * service time) / (1 - arrival rate * service time)

For the given problem, the average queue length is:

Average queue length = (50 * 35) / (1 - 50 * 35)

= 175

Since the average queue length is greater than 10 students, the introduction of an extra checkpoint is justifiable.

Learn more about distribution on:

brainly.com/question/9123296

#SPJ9

Pavlova-9 [17]1 year ago
4 0
I think its 101010183727382
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