Respuesta :
Answer:
9.08% probability that in a day, there are 14 births. So it does not appear likely that on any given day, there will be exactly 14 births.
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 4386 births.
An year has 365 days. So [tex]\mu = \frac{4386}{365} = 12.02[/tex]
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?
This is P(X = 14).
[tex]P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}[/tex]
[tex]P(X = 14) = \frac{e^{-12.02}*(12.02)^{14}}{(14)!} = 0.0908[/tex]
9.08% probability that in a day, there are 14 births. So it does not appear likely that on any given day, there will be exactly 14 births.
