Question

At an emergency service center in a large city, calls come in at an average rate of four calls per minute. Assume that the time that elapses from one call to the next has the exponential distribution. The probability that more than 40 calls occur in an eight-minute period is

Answer 1

1 minute = 4calls(approx)

Therefore, 8 minutes=8×4= 32 calls

Probality = total calls /total time

=>40/8

=> 5 calls (answer(

Answer 2

Concept: The Poisson distribution deals with the amount of occurrences during mounted amount of your time, and also the exponential distribution deals with the time between occurrences of sequential events as time flows by unending.

Find: Calculate the probability that more than 40 calls occur in an eight-minute period.

Solution:

Let Y= the quantity of calls that occur throughout associate eight minute amount.

Since there's a median of 4 calls per minute, there's a median of (8)(4)=32 calls throughout every eight minute amount.

Hence, Y∼Poisson(32). Therefore, P(Y is greater than 40)=1−P(Y≤40)=1−0.9294=0.0707.

1−poissoncdf(32,40).=0.0707

Final answer: the probability that more than 40 calls occur in an eight-minute period is 0.70707.

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