THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING:
Suppose you know that the number of complaints coming into a phone center averages 4.2 every ten minutes.Assume that the number of calls follows the Poisson distribution.
-What is the probability that there are exactly four calls during the next ten minutes?
A)0.194
B)0.172
C)0.156
D)0.134

Question

Quizplus · Accepted Answer

The probability of observing exactly k events in a fixed interval of time is given by the formula for the Poisson distribution: P(k; λ) = (e^(-λ) * λ^k) / k!, where λ is the average number of events (4.2 in this case), k is the number of events of interest (4 calls), and e is the base of the natural logarithm (approximately 2.71828). Plugging the values into the formula gives P(4; 4.2) = (e^(-4.2) * 4.2^4) / 4! ≈ 0.194.