Respuesta :
Answer:
There is a 44.22% probability that at least 2 tornados occurred in the period from January 1 to June 30.
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 this problem, we have that:
In a year, there tends to be 3 tornados. From January 1 to June 30, it is half a year. So [tex]\mu = 1.5[/tex]
Calculate the probability that at least 2 tornados occurred in the period from January 1 to June 30.
Either there were less than two tornados on this interval, or there were two or more. The sum of the probabilities of these events is decimal 1. So:
[tex]P(X < 2) + P(X \geq 2) = 1[/tex]
[tex]P(X \geq 2) = 1 - P(X < 2)[/tex]
In which
[tex]P(X < 2) = P(X = 0) + P(X = 1)[/tex]
So
[tex]P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}[/tex]
[tex]P(X = 0) = \frac{e^{-1.5}*(1.5)^{0}}{(0)!} = 0.2231[/tex]
[tex]P(X = 1) = \frac{e^{-1.5}*(1.5)^{1}}{(1)!} = 0.3347[/tex]
[tex]P(X < 2) = P(X = 0) + P(X = 1) = 0.2231 + 0.3347 = 0.5578[/tex]
Finally
[tex]P(X \geq 2) = 1 - P(X < 2) = 1 - 0.5578 = 0.4422[/tex]
There is a 44.22% probability that at least 2 tornados occurred in the period from January 1 to June 30.
