Question

The arrivals of patients at a walk-in clinic between 1:00 and 2.00 PM follows a Poisson process with the mean of 10.5. (a) What is the probability that 15 patients arrive at the clinic between 1:00 and 2:00 PM? Round your answer to three decimal places leg. 98.765)

Answer 1

To find the probability that more than eight patients arrive during a half-hour period, we can use the Poisson distribution. The probability is approximately 0.0311.

Step-by-step explanation:

To find the probability that more than eight patients arrive during a half-hour period, we can use the Poisson distribution. The mean for the Poisson distribution is given as 30, which represents the average number of patients arriving in a half-hour period. We can calculate the probability using the formula P(X > 8) = 1 - P(X ≤ 8), where X is the number of patients.

Substituting the values, we have P(X > 8) = 1 - P(X ≤ 8) ≈ 0.0311. Therefore, the probability that more than eight patients arrive during a half-hour period is approximately 0.0311.