Question

The number of 911 calls in Butte, Montana, has a Poisson distribution with a mean of 6 calls per hour. The probability of receiving exactly 5911 calls in an hour is: (Keep four decimal places)

Answer 1

The probability of receiving exactly 5 calls in an hour at Butte, Montana's 911 call center, following a Poisson distribution with a mean of 6 calls per hour, is approximately 0.1606 or 16.06%.

Step-by-step explanation:

The student's question is related to the Poisson distribution, a statistical concept used to model the number of events that occur independently within a fixed interval of time or space. Given that Butte, Montana, has an average of 6 911 calls per hour (which is the mean rate λ of the Poisson distribution), the probability of receiving exactly 5 911 calls in an hour can be calculated using the Poisson probability mass function:

P(X = k) = (λ^k * e^-λ) / (k!)

For k = 5:

P(X = 5) = (6^5 * e^-6) / (5!) = (7776 * e^-6) / 120 ≈ 0.1606

Here, e is the base of the natural logarithm, and k! (5! in this case) is the factorial of k.

The probability of exactly 5 calls in an hour is about 0.1606 (or 16.06% when converted to percentage), not 5911 calls as there might be a typo in the question.