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 12 people per hour. The inter-arrival time, X, is defined as the time that passes between successive arrivals of patients seeking medical attention.

a) It has been 4 minutes since the last person seeking medical attention arrived at the ER. What is the probability that at least 11 minutes (in total) will pass until the next medical-attention-seeking person passes through the ER doors?

Answer 1

To find the probability that at least 11 minutes will pass until the next person arrives, we can use the exponential distribution. The exponential distribution is often used to model the time between events occurring at a constant rate. In this case, the mean number of people arriving per hour at the ER is given as 12. We can use the exponential distribution formula to find the desired probability.

Step-by-step explanation:

To find the probability that at least 11 minutes will pass until the next person arrives, we can use the exponential distribution. The exponential distribution is often used to model the time between events occurring at a constant rate.

In this case, the mean number of people arriving per hour at the ER is given as 12. We can use the exponential distribution formula: P(X > t) = e^(-λt), where X is the time between events, t is the desired time, and λ is the rate of events per unit time.

The rate of events per hour can be calculated by taking the reciprocal of the mean: λ = 1/12. Plugging in the values, we have P(X > 11) = e^(-1/12 * 11), which can be evaluated as approximately 0.406.