Answer: 0.9577 ≈ 95.77%
Step-by-step explanation:
This can be solved by the Poisson distribution formula for random variables when the mean outcome of such variables are given.
The Poisson Formula is denoted by :
P(X=K) = e^-λ × (λ^k/k!)
Where e = exponential factor y 2.71828
λ = mean/ average outcome = 8
k = varied outcome.
To find the probability of more than 3,we find the probability of 3 or less, sum it then subtract from 1,that is P(X>3) = 1 - P(X≤3)
When k=0
P(X=0) = e^-8 × (8^0/0!) = 0.000335
When k=1
P(X=1) = e^-8 × (8¹/1!) = 0.00268
When k=2
P(X=2) = e^-8 × (8²/2!) = 0.0107
When k=3
P(X=3) = e^-8 × (8³/3!) = 0.0286
P(X≤3) = 0.00035 + 0.00268 + 0.0107 + 0.0286 = 0.0423
Hence, P(X>3) = 1 - 0.0423 = 0.9577 ≈ 95.77%
