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8. Let X be the number of cars per minute passing a certain point of some road between 8am and 10am on a Sunday. Assume that X has a Poisson distribution with mean 5. Find the probability of observing 3 or fewer cars during any given minute.

Respuesta :

akiran007

Answer:

P (3 or fewer) =0.2650

Step-by-step explanation:

Mean = x` = 5

The Poisson distribution formula Ā is given by

P(X) = e-Ė£` x`Ė£/ x!

The mean is 5 and the X takes the values 0,1,2,and 3 which means 3 or fewer, so we add the probability of all the values of X to get the desired Value of X.

P(3 or fewer ) = e-āµ (5)Ā³/3!+ Ā e-āµ (5)Ā²/2! +e-āµ (5)/1!+e-āµ (5)ā°/0!

Putting the Values

P (3 or fewer) = 0.006737 . 125 / 6 + 0.006737 . 25 / 2 +0.006737 . 5 / 1 + 0.006737 . 1 / 1

P (3 or fewer) = 0.140374 + 0.08422+ 0.03369 +0.006737

P (3 or fewer) =0.2650

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