The Answer to the Question
is below this banner.
Here's the Solution to this Question
i) it is a poisson distribution. This is so because it defines the probability of a number of independent events occurring in a fixed time. It shows how many times an event is likely to occur over a specified period.
ii) x is a poisson variable with mean = 3, so the probability mass function of of x is
p(X=x) = (e-3 * 3x)/(x!), x= 0,1, 2,3, ......
iii) The possible values of x are 0,1,2,3,4 ....
iv) we define p(x≥3) = 1- p(x=0) - P(x=1) - P(x=2)
= 1- ( (e-3 *30) - (e-3 * 31) - ( (e-3 * 32) /2) )
=0.5767 which is the required solution.