The number x of people entering the intensive care unit at a particular hospital
ID: 3149757 • Letter: T
Question
The number x of people entering the intensive care unit at a particular hospital on any day has a Poisson probability distribution with the mean equal to four persons per day.
A) What is the probability that the number of people entering the intensive care unit on a particular day is two? (Round answer to three decimal places)
B) What is the probability that the number of people entering the intensive care unit on a particular day is less than or equal to two? (Round your answer to three decimal places)
Explanation / Answer
as given the mean for the poisson dirtribution = 4
the formula for poisson distribution =
a) we need to find p(x=2) = 4^2*e^(-4)/2! = 0.1465
b) here we need to find the p(x<=2) = p(0)+p(1)+p(2)
p(0) = 4^0*e^(-4)/0! = 0.0183
p(1) = 4^1*e^(-4)/1! = 0.0732
hence p(x<=2) = 0.0183+0.0732+0.1465
= 0.238