Question

The number of people arriving for treatment in one hour at an emergency room can be modeled by a random variable X. Mean of X is 5.

a) What’s the probability that at least 4 arrivals occurring?

b) Suppose the probability of treating no patient in another emergency room is 0.05, which emergency room could be busier? Why?

Answer 1

given that

The number of people arriving for treatment in one hour at an emergency room can be modeled by a random variable X

here mean of X=5

so X is Poisson distribution with

Hence

a)

Here we have to find P(X>4)

now

b)

since the probability of treating no patient in another emergency room is 0.05

while we check that probability that there is no patient treating for that we need P(X=0)

now

since probability of treating no patient at first emergency room is 0.007 which is less than that of 2nd emergency no.(0.05)

Hence first emergecny room is more busy than 2nd one.