On weekdays during the academic year, the number of telephone calls at the main University call center follows a Poisson Point Process with a mean of 4 calls per m

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On weekdays during the academic year, the number of telephone calls at the main University call center follows a Poisson Point Process with a mean of 4 calls per minute.

What is the probability that the time between calls exceeds 30 seconds?
O 0.1353
O 0.8464
O 0.4587
O There isn't sufficient information to answer this question
Transcribed Image Text:What is the probability that the time between calls exceeds 30 seconds? O 0.1353 O 0.8464 O 0.4587 O There isn't sufficient information to answer this question
Expert Solution
Step 1

The number of telephone calls at the main University call center follows a Poisson Point Process with a mean of 4 calls per minute.

Let us consider, the number of calls per second is,

λ=4/60=0.0667 since, 1 minute=60 seconds

Let us define the random variable X as the time between the calls follows Exponential distribution with λ=0.0667

The density function for X is,

f(X=x)=λeλx             

         =0.0667e0.0667x

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