(Poisson/Exponential) The number of automobiles that arrive at a certain intersection per minute has a Poisson distribution with mean 3. Interest centers around the time that elapses before 9 automo- biles appear at the intersection.

What is the probability that more than 9 automobiles appear at the intersection during any given minute of time?

0.011

Step-by-step explanation:

Let X represents the number of automobiles that arrive at a certain intersection per minute

X follows a Poisson distribution with a mean of 3.

Calculating the probability that more than 9 automobiles appear at the intersection during any given minute of time;

P(X > 9) = 1 - P(X ≤ 9)

P(X>9) = 1 - ∑(e^-λ * λ^x)/x! For x = 0 to 9.

P(X>9) = 1 - (P(X=0) + P(X=1) ++P(X=9))

P(X>9) = 1 - ((e^-3 * 3^0)/0! + (e^-3 * 3^1)/1! + + (e^-3 * 3^9)/9!))

P(X>9) = 1 - (0.049787068367863 + 0.149361205103591 + 0.224041807655387 + 0.224041807655387 + 0.168031355741540 + 0.100818813444924 + 0.050409406722462 + 0.021604031452483 + 0.008101511794681 + 0.002700503931560)

P(X>9) = 0.001102488130122

P(X>9) = 0.0011 --- Approximated

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step-by-step explanation: