In Exercises 21–25, find the indicated probabilities using the geometric distrib
ID: 3128026 • Letter: I
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