Question

"​​​​General Hospital has noted that they admit an average of 7 patients per hour. What is the probability that during the next hour less than 2 patients will be admitted?

Answer 1

To find the probability that during the next hour less than 2 patients will be admitted, we can use the Poisson distribution formula. In this case, the average number of patients admitted per hour is 7, and we need to calculate P(X<2), which is the sum of probabilities for k=0 and k=1.

Step-by-step explanation:

To find the probability that during the next hour less than 2 patients will be admitted, we can use the Poisson distribution formula:

P(X=k) = (e^(-λ) * λ^k) / k!

In this case, the average number of patients admitted per hour (λ) is 7. We need to calculate P(X<2), which is the sum of probabilities for k=0 and k=1:

P(X<2) = P(X=0) + P(X=1)

P(X=0) = (e^(-7) * 7^0) / 0! = e^(-7) = 0.00091188

P(X=1) = (e^(-7) * 7^1) / 1! = 0.00638317

Therefore, P(X<2) = 0.00091188 + 0.00638317 = 0.00729505