I need to know the probability of this poisson distribution?

Question

For a particular hospital in a large city, the staff on hand cannot accommodate the patient traffic if there are more than 10 emergency cases in a given hour. It is assumed that patient arrival follows a Poisson process, and on average, 5 emergencies arrive per hour. What is the probability that in a given hour the staff can no longer accommodate the traffic?

Answer 1

You could use the formula for P
P(n,5) = exp(-5)*5^n / n!
Add it up for n = 0 to 10 and you get that hte prob of n being less than or equal to 10 is 0.9863

So P(n > 10) = 0.0137

Answer 2

The probability of exactly k occurrences in a given time period when the mean number of occurrences in a time period is λ is given by:

P(k|λ) = [(λ^k)*e^(-λ)] / k!

So for λ = 5, the probability of not being able to accomodate the traffic is:

P(k>10 | 5) = 1 - P(k≤10)

..... ...... ..... ...... ..10
P(k>10 | 5) = 1 - Σ{[(5^n)*e^(-5)] / n!} = 0.013695269
..... ...... ..... ...... .n=0