An operations analyst counted the number of arrivals per minute at an ATM in each of 30 randomly chosen minutes. The results were: 0, 3, 3, 2, 1, 0, 1, 0, 0, 1, 1, 1, 2, 1, 0, 1, 0, 1, 2, 1, 1, 2, 1, 0, 1, 2, 0, 1, 0, 1. For the Poisson goodness-of-fit test, what is the expected frequency of the data value X = 1?
A)Impossible to determine.
B)11.04
C)1.00
D)2.47

Question

Quizplus · Accepted Answer

To find the expected frequency of the data value X = 1 for a Poisson distribution, we first calculate the mean (λ) of the given data. The mean is the total number of arrivals divided by the total number of minutes observed. Summing up the arrivals gives us 0+3+3+2+1+0+1+0+0+1+1+1+2+1+0+1+0+1+2+1+1+2+1+0+1+2+0+1+0+1 = 30. There are 30 minutes, so the mean λ = 30/30 = 1. The expected frequency for a Poisson distribution with mean λ for the value X = k is given by E(X=k) = n * (e^(-λ) * λ^k / k!), where n is the total number of observations (30 in this case), e is the base of the natural logarithm, and k is the value for which we are finding the expected frequency. For X = 1, this becomes E(X=1) = 30 * (e^(-1) * 1^1 / 1!) = 30 * (1/e) ≈ 30 * 0.368 = 11.04.

An Operations Analyst Counted the Number of Arrivals Per Minute