Question

The number of people arriving per hour at the emergency room (ER) of a local hospital seeking medical attention can be modeled by the Poisson distribution, with a mean of 14 people per hour. The inter-arrival time, XX, is defined as the time that passes between successive arrivals of patients seeking medical attention

How much time in minutes would you expect to pass between the arrival of successive patients seeking medical attention at this ER, in any given hour? Enter your answer to two decimals.

Answer 1

The expected inter-arrival time between successive patients at an emergency room with a Poisson distribution mean of 14 people per hour is 4.29 minutes per person (rounded to two decimal places).

Step-by-step explanation:

The question concerns the Poisson distribution and the exponential distribution, both of which are concepts in probability theory, a branch of mathematics. Specifically, the question is asking for the expected inter-arrival time, in minutes, between successive patients seeking medical attention at an emergency room, given the average number of arrivals per hour follows the Poisson distribution with a mean of 14 people per hour.

To find the expected inter-arrival time, we utilize the fact that the inter-arrival times in a Poisson process are exponentially distributed. The rate λ for the exponential distribution is the same as the mean of the Poisson distribution, which is 14 people per hour. The expected inter-arrival time is the inverse of this rate. To convert this rate to minutes, we perform the calculation 1/14 and then multiply by 60 to get the time in minutes.

The expected inter-arrival time is calculated as follows:

Expected inter-arrival time = 1/mean rate = 1/λ

So, for a mean of 14 people per hour, the expected inter-arrival time is:

1/14 hours per person * 60 minutes per hour = 4.29 minutes per person (to two decimal places).