In Exercises 21–25, find the indicated probabilities using the geometric distrib

Question

In Exercises 21–25, find the indicated probabilities using the geometric

distribution, the Poisson distribution, or the binomial distribution. Then determine

whether the events are unusual. If convenient, use a table or technology to find the

probabilities.

During a 73-year period, tornadoes killed about 0.28 people per day in the

United States. Assume this rate holds true today and is constant throughout

the year. Find the probability that the number of people in the United

States killed by a tornado tomorrow is (a) exactly zero, (b) at most two, and

(c) more than one.

Explanation / Answer

Possion Distribution
PMF of P.D is = f ( k ) = e- x / x!
Where   
= parameter of the distribution.
x = is the number of independent trials
a.
P( X = 0 ) = e ^-0.28 * 0.28^0 / 0! = 0.7558

b.
P( X < = 2) = P(X=2) + P(X=1) + P(X=0)
= e^-0.28 * 0.28 ^ 2 / 2! + e^-0.28 * 0 ^ 1 / 1! + e^-0.28 * ^ 0 / 0!
= 0.997

c.
P( X < = 1) = P(X=1) + P(X=0)   
= e^-0.28 * 0.28 ^ 1 / 1! + e^-0.28 * 0 ^ 0 / 0!
= 0.9674
P( X > 1) = 1 -P ( X <= 1) = 1 - 0.9674 = 0.0326

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