Question

At an urgent care facility, patients arrive at an average rate of one patient every seven minutes. Assume that the duration between arrivals is exponentially distributed.

a. Exponential distribution with mean 7 minutes

b. Normal distribution with mean 7 minutes

c. Poisson distribution with mean 7 minutes

d. Exponential distribution with mean 1/7 minutes

Answer 1

The distribution that can be used to model the time between arrivals at an urgent care facility is the Exponential distribution with mean 7 minutes. To find the probabilities associated with the time between visits, we can use the formulas provided.

Step-by-step explanation:

The distribution that can be used to model the time between arrivals at an urgent care facility is the Exponential distribution with mean 7 minutes (option a).

1. To find the probability that the time between two successive visits is less than two minutes, we can use the formula: P(T < 2) = 1 - e-2/7.
2. To find the probability that the time between two successive visits is more than 15 minutes, we can use the formula: P(T > 15) = 1 - P(T ≤ 15) = 1 - (1 - e-15/7).
3. If 10 minutes have passed since the last arrival, we can find the probability that the next person will arrive within the next five minutes by using the formula: P(T < 5 | T > 10) = P(T < 5) / P(T > 10) = (1 - e-5/7) / (1 - e-10/7).
4. To find the probability that more than eight patients arrive during a half-hour period, we can use the Poisson distribution with a mean of 30 patients in a one-hour period, and then calculate P(X > 8) = 1 - P(X ≤ 8).