Respuesta :
Answer:
10.10% probability that in a day, there are 13 births. It is not very likely that in a day there will be exactly 13 births, but also not unlikely(lower than 5%).
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:
[tex]P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}[/tex]
In which
x is the number of sucesses
e = 2.71828 is the Euler number
[tex]\mu[/tex] is the mean in the given time interval.
In a recent year, a hospital had 4224 births.
An year has 365 days, so [tex]\mu = \frac{4224}{365} = 11.5726[/tex]
Probability that in a day, there are 13 births.
This is P(X = 13).
[tex]P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}[/tex]
[tex]P(X = 13) = \frac{e^{-11.5726}*(11.5726)^{13}}{(13)!} = 0.1010[/tex]
10.10% probability that in a day, there are 13 births. It is not very likely that in a day there will be exactly 13 births, but also not unlikely(lower than 5%).
