Homework SourseRecent crime reports indicate that 55 motor vehicle thefts o
Recent crime reports indicate that 5.5 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.
Calculate the probability exactly two thefts occur in a minute.(Round your answer to 3 decimal places.)
What is the probability there are no thefts in a minute? (Round your answer to 3 decimal places.)
What is the probability there is three or less theft in a minute? (Round your answer to 3 decimal places.)
| Recent crime reports indicate that 5.5 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. |
Solution
Given X~Poisson(mean=5.5)
P(X=x)=(5.5^x)*exp(-5.5)/x!
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(a) P(X=2) = (5.5^2)*exp(-5.5)/2= 0.062
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(b) P(X=0) = (5.5^0)*exp(-5.5)/1=0.004
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(c) P(X<=3) = P(X=0)+P(X=1)+P(X=2)+P(X=3)
= (5.5^0)*exp(-5.5)/1 + (5.5^1)*exp(-5.5)/1 + (5.5^2)*exp(-5.5)/2 + (5.5^3)*exp(-5.5)/6
=0.202
