Question

Suppose that the number of airplanes arriving at an airport per minute is a Poisson process. The average number of airplanes arriving per minute is 3. The probability that exactly 6 planes arrive in the next minute is =POISSON(6,3,TRUE).

a. True
b. False

Answer 1

The final answer is False because the provided formula =POISSON(6,3,TRUE) deviates from the standard Poisson distribution parameters, introducing an unconventional third parameter (TRUE) that is not part of the standard probability mass function. Consequently, this results in an inaccurate calculation of the probability of exactly 6 planes arriving.

Step-by-step explanation:

The correct formula to calculate the probability of exactly k events occurring in a Poisson process with an average rate of λ is given by the probability mass function (PMF):

`\[ P(X = k) = (e^(-\lambda) \cdot \lambda^k)/(k!) \]`

In this case, the average rate (λ) is 3, and we want to find the probability of exactly 6 planes arriving (k = 6). Plugging these values into the formula:

`\[ P(X = 6) = (e^(-3) \cdot 3^6)/(6!) \]`

Calculating this expression gives the actual probability of exactly 6 planes arriving in the next minute. However, the expression =POISSON(6,3,TRUE) seems to use different parameters or a different calculation method, resulting in an incorrect answer. Therefore, the correct response to the given question is False.

It's crucial to use the proper formula for the Poisson distribution to ensure accurate probability calculations. In this scenario, the probability can be determined through the standard Poisson PMF, and any deviation from this approach may yield an inaccurate result.

Therefore, the final answer is false.