3 Recent crime reports indicate that 3.5 motor vehicle thefts occur each minute

Question

3 Recent crime reports indicate that 3.5 motor vehicle thefts occur each minute in the United States. Assume that the distribution of thefts per minute can be approximated by the Poisson probability distribution. a. Calculate the probability exactly three thefts occur in a minute. (Round your probability to 3 decimal places.) Probability b. What is the probability there are five or more thefts in a minute? (Round your probability to 3 decimal places.) Probabilit c. What is the probability there is two or less thefts in a minute? (Round your probability to 3 decimal places.) robabilit

Explanation / Answer

Given X~Poisson(mean=3.5)

p(x=k)=k*e-/k!

(a) P(X=3) = (3.5^3)*exp(-5.5)/3= 0.2157

b)p(x>=5)=1-p(x=5) -p(x=4)-p(x=3)-p(x=2)-p(x=1)-p(x=0)

=1-0.7255

=0.2745

c)p(x<=2)=p(x=2)+p(x=1)+p(x=0)

=0.3208

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