Question

Infected patients with a certain virus arrive in a hospital according to a Poisson process with an average rate of 20.2 per day. The hospital management is planning the level of resources that they need in the coming weeks. As a part of this planning effort, they are interested to know what is the probability of receiving 3 patients in 1.4 hours? (Assume each day is 24 hours) state your answer in decimal format not percentage

Answer 1

The probability of receiving 3 patients in 1.4 hours, given an average rate of 20.2 per day, is approximately 0.0903.

Step-by-step explanation:

To find the probability of receiving 3 patients in 1.4 hours, we need to convert the average rate of 20.2 patients per day to an average rate per hour. Since each day has 24 hours, the average rate per hour can be calculated as 20.2 divided by 24: 20.2/24 = 0.8417.

Now, we can use the Poisson distribution formula to calculate the probability. The formula is P(x; λ) = (e^-λ * λ^x) / x!, where x is the number of events, λ is the average rate per unit of time, e is the base of the natural logarithm (approximately 2.71828), and x! represents the factorial of x.

In this case, x = 3 and λ = 0.8417 * 1.4 (since 1.4 hours is the time period we are interested in).

Therefore, P(3; 0.8417 * 1.4) ≈ 0.0903.