Answer: 0.12
Explanation:
Poisson distribution is used to approximate the probability of a given number of event with a known average occurrence. The Formula for this distribution is denoted by:
P(X=k) = e^-λ × (λ^k/k!)
Where k = variable probability value.
λ = average occurrence of event
e = exponential value = 2.71828
For determining on the number of accidents greater than 2,we determine for when k = 0,1,2 and subtract the answer from 1, that is P(X>2) = 1 - P(X≤2)
When k=0,
P(X=0) = e^-1.2 × (1.2^0/0!) = 0.3012
When k=1
P(X=1) = e^-1.2 × (1.2^1/1!) = 0.3614
When k=2
P(X=2) = e^-1.2 × (1.2²/2!) = 0.2169
When k=0,1,2, the sum of probability = 0.3012 + 0.3614 + 0.2169 = 0.8795.
Hence, P(X>2) = 1 - 0.8795 = 0.1205 ≈ 0.12