Question

Patients arrive at hospital accident and emergency at random at an average rate of 6 per hour. Find the probability that, during any 60-minute period, the number of patients arriving at the hospital accident and emergency department is at least 2. Round off answers to 4 decimal places.

Answer 1

This is a Poisson distribution with $\lambda=6.$

$P(X\ge2)=1-P(X=0)-P(X=1)=1-e^{-6}(\frac{6^0}{0!}+\frac{6^1}{1!})=0.9827.$