Answer:
P (3 or fewer) =0.2650
Step-by-step explanation:
Mean = x` = 5
The Poisson distribution formula is given by
P(X) = e-ˣ` x`ˣ/ 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-⁵ (5)³/3!+ e-⁵ (5)²/2! +e-⁵ (5)/1!+e-⁵ (5)⁰/0!
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
