Respuesta :
Answer:
0.1606 = 16.06% probability that the number of births in any given minute is exactly five.
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 interval.
In this question:
We only have the mean during an interval, and this is why we use the Poisson distribution.
The mean number of births per minute in a given country in a recent year was about 6.
This means that [tex]\mu = 6[/tex]
Find the probability that the number of births in any given minute is exactly five.
This is P(X = 5). So
[tex]P(X = 5) = \frac{e^{-6}*6^{5}}{(5)!} = 0.1606[/tex]
0.1606 = 16.06% probability that the number of births in any given minute is exactly five.
