Answer:
The probability that the next tornado comes within the next 9 months is 1-0.1054 = 0.8946
Step-by-step explanation:
In 12 months the average of tornadoes is 3.0, does in 9 months, we can conclude, applying a rule of three, that the average of tornaoes is 3.0*9/12 = 2.25. We may assume that the distribution of Tornadoes is a period of time is Poisson. Lets call X the amount of Tornadoes in a 9 month period. X has distribution Poisson with parameter λ=2.25.
The probability that the next tornado comes within the next 9 months is equal to the probability of X being greater than or equal to 1. However P(X≥1) = 1-P(X=0), and
[tex] P(X=0) = \frac{e^{-2.25}*{2.25}^{0}}{0!} = 0.1054 [/tex]
Thus, the probability that the next tornado comes within the next 9 months is 1-0.1054 = 0.8946.
