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Sagot :
Answer:
0.1512 = 15.12% probability that fewer than four tornadoes occur in a three-week period.
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 a given region, the number of tornadoes in a one-week period is modeled by a Poisson distribution with mean 2
Three weeks, so [tex]\mu = 2*3 = 6[/tex]
Calculate the probability that fewer than four tornadoes occur in a three-week period.
This is:
[tex]P(X < 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3)[/tex]
In which
[tex]P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}[/tex]
[tex]P(X = 0) = \frac{e^{-6}*6^{0}}{(0)!} = 0.0025[/tex]
[tex]P(X = 1) = \frac{e^{-6}*6^{1}}{(1)!} = 0.0149[/tex]
[tex]P(X = 2) = \frac{e^{-6}*6^{2}}{(2)!} = 0.0446[/tex]
[tex]P(X = 3) = \frac{e^{-6}*6^{3}}{(3)!} = 0.0892[/tex]
Then
[tex]P(X < 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) = 0.0025 + 0.0149 + 0.0446 + 0.0892 = 0.1512[/tex]
0.1512 = 15.12% probability that fewer than four tornadoes occur in a three-week period.
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