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# Quantitative methods problem?

General Hospital has noted that they admit an average of 8 patients per hour. For the last 30 minutes, no patient has been admitted. What is the probability that no patients will be admitted in the next 1 hour?

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- PuzzlingLv 76 months ago
First, I'll assume that the patient arrivals follow a Poisson distribution. Also, I'll assume that arrivals are independent so the prior history during the last 30 minutes should be independent of what will happen in the next hour.

The solution of the Poisson distribution function is given by the formula:

poisson(n,λ) = [λ^n * e^(-λ)] / n!

You want to know the probability of exactly 0 arrivals (n = 0) when the standard rate in 1 hour is 8 arrivals (λ = 8)

poisson(0,8) = 8^0 * e^(-8) / 0!

= 1 * e^(-8) / 1

= 1/e^8

≈ 0.0003354

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