Question

calls arrive at lynn ann fish's hotel switchboard at a rate of 2.0 per minute. the average time to handle each is 10 seconds. there is only one switchboard operator at the current time. the poisson and negative exponential distributions appear to be relevant in this situation. what is the probability, as a percent, that the operator is busy

Answer 1

The probability that the operator is busy is 33.33% if the call rate is 2 per minute and average time to handle is 10 seconds.

Given rate of calls 2 per minute and average time to handle a call is 10 seconds.

We have to find the probability that the operator is busy.

Probability is the chance of happening an event among all the events possible. The value of probability lies between 0 and 1.

Probability= number of items/ total items

If rate is 2 per minute then the customers handled in 1 hour=2*60=120

The average time to handle a call=10 seconds.

Therefore customers to be handled in 1 hour=360 (10*6*60)

Probability that the operator is busy is as under:

Probability=λ/μ

=120/360

=1/3

=1/3*100

=33.33%

Hence the probability that the operator is busy is 33.33%.

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