Question

In a recent​ year, a hospital had 4391 births. (A) Find the mean number of births per​ day, (B) then use that result and the Poisson distribution to find the probability that in a​ day, there are 15 births. (C) Does it appear likely that on any given​ day, there will be exactly 15 ​births?

Answer 1

a)

Mean number of birth per day = 4391 / 365 = 12.0301

b)

Poisson probability distribution is

P(X) = e^-X / X!

P (X = 15) = e^-12.0301 * 12.0301¹⁵ / 15!

= 0.0729

c)

Since this probability is greater than 0.05, event is usual.

It appears likely that on any given day, there will be exactly 15 births.