The Poisson distribution is a discrete distribution that expresses the probability of a fixed number of events occurring in a fixed interval.For example,suppose we want to model the number of arrivals per minute at the campus dining hall during lunch.We observe the actual arrivals in 200 one-minute periods in 1 week.The sample mean is 3.8 and the results are shown below. The probabilities based on a Poisson distribution with a mean of 3.8 are shown below. What is the expected count for 0 arrivals?

A) 10
B) 200
C) 4
D) None of the above

Question

The Poisson distribution is a discrete distribution that expresses the probability of a fixed number of events occurring in a fixed interval.For example,suppose we want to model the number of arrivals per minute at the campus dining hall during lunch.We observe the actual arrivals in 200 one-minute periods in 1 week.The sample mean is 3.8 and the results are shown below.

The probabilities based on a Poisson distribution with a mean of 3.8 are shown below.

What is the expected count for 0 arrivals?

A) 10
B) 200
C) 4
D) None of the above

danielle wickman · Accepted Answer

Final Answer : C, Explanation :  The Poisson distribution expresses the probability of a fixed number of events occurring in a fixed interval. The sample mean is 3.8, which means that on average, 3.8 arrivals occur per minute during lunch at the campus dining hall. In order to find the expected count for 0 arrivals, we can use the formula for the Poisson distribution: P(X = 0) = e^(-λ) * λ^0 / 0! where λ is the mean number of arrivals per minute. Plugging in 3.8 for λ, we get P(X = 0) = e^(-3.8) * 3.8^0 / 0! = 0.022 (rounded to three decimal places). This means that the probability of having 0 arrivals in a minute is 0.022, or 2.2%. In 200 one-minute periods, we would expect to have 0 arrivals during lunch 0.022 * 200 = 4.4 times. Since we cannot have a fractional number of arrivals, we round down to the nearest integer, which is 4. Therefore, the expected count for 0 arrivals is 4. Choice C is the correct answer.

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