Suppose the number of patients going to a particular emergen

Suppose the number of patients going to a particular emergency room between 2 a.m. and 3 am. on a Thursday (any Thursday) can be well-approximated by a Poisson distribution with lambda= 5. What is the probability the number of patients who go to that emergency room on a given Thursday during that time period is at least 4?

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( X < 4) = P(X=3) + P(X=2) + P(X=1) + P(X=0)
= e^-5 * 2 ^ 3 / 3! + e^-5 * ^ 2 / 2! + e^-5 * ^ 1 / 1! + e^-5 * ^ 0 / 0!
= 0.265
P( X > = 4 ) = 1 - P (X < 4) = 0.735