large manufacturing plant has averaged 7 reportable accident

large manufacturing plant has averaged 7 “reportable accident” per month. Suppose that accident counts over time follow a Poisson distribution with mean 7 per month. (a)What is the probability of exactly 7 accidents in a month? (b)What is the probability of at least one accident in a month?

Solution

Possion Distribution
PMF of P.D is = f ( k ) = e- x / x!
Where   
= parameter of the distribution.
x = is the number of independent trials
a)
P( X = 7 ) = e ^-7 * 7^7 / 7! = 0.15
b)
P( X < 1) = P(X=0) +   
= e^-7 * 7 ^ 0 / 0! +
= 0.00091
P( X > = 1 ) = 1 - P (X < 1) = 0.99909