Answer:
0.9999985 = 99.99985% probability that in a day, there will be at least 1 birth.
Step-by-step explanation:
In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:
In which
x is the number of sucesses
e = 2.71828 is the Euler number
is the mean in the given interval.
Assume that the mean number of births per day at this hospital is 13.4224.
This means that ![\mu = 13.4224](https://tex.z-dn.net/?f=%5Cmu%20%3D%2013.4224)
Find the probability that in a day, there will be at least 1 birth.
This is:
![P(X \geq 1) = 1 - P(X = 0)](https://tex.z-dn.net/?f=P%28X%20%5Cgeq%201%29%20%3D%201%20-%20P%28X%20%3D%200%29)
In which
Then
![P(X \geq 1) = 1 - P(X = 0) = 1 - 0.0000015 = 0.9999985 ](https://tex.z-dn.net/?f=P%28X%20%5Cgeq%201%29%20%3D%201%20-%20P%28X%20%3D%200%29%20%3D%201%20-%200.0000015%20%3D%200.9999985%0A)
0.9999985 = 99.99985% probability that in a day, there will be at least 1 birth.