Many people keep a garden even in a city The population mean

Many people keep a garden even in a city. The population mean for the number of people who keep a garden in any random block of the city is 4.2. Find the probability that on a randomly chosen block over 3 people keep a garden.

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
p = 4.2

P( X < 3) = P(X=2) + P(X=1) + P(X=0)   
= e^-4.2 * 3 ^ 2 / 2! + e^-4.2 * ^ 1 / 1! + e^-4.2 * ^ 0 / 0! +
= 0.2102
P( X > = 3 ) = 1 - P (X < 3) = 0.7898