Question

In a recent​ year, a hospital had 4386 births. Find the mean number of births per​ day, then use that result and the Poisson distribution to find the probability that in a​ day, there are 14 births. Does it appear likely that on any given​ day, there will be exactly 14 ​births? The mean number of births per day is nothing.

Answer 1

Answer:

Mean number of births = 12.02 births per day.

P(X=14) = 0.0908=9.08%

Not likely

Step-by-step explanation:

Mean number of births (λ):

$\lambda=\frac{4386}{365}\\ \lambda=12.02\ births/day$

Assuming a Poisson distribution, the probability of X = 14 successes (births on a single day) is determined by:

$P(X=x) = \frac{\lambda^xe^{-\lambda}}{x!} \\P(X=14) = \frac{12.02^{14}e^{-12.02}}{14!}\\P(X=14) =0.0908$

The probability that there are exactly 14 births in a day is 9.08%, which is not likely.