3
The number of combines sold each year by a dealership that specialises in agricultural equipment is a Poisson random variable with an average of 4.
What is the probability that the dealership will sell:
3.2More than three combines in a period of six months.
To find the probability that the dealership will sell more than three combines in a period of six months, we can use the Poisson distribution formula:
P(X > 3) = 1 - P(X ≤ 3)
Where X is the number of combines sold in a period of six months.
First, we need to find the probability of selling 0, 1, 2, or 3 combines in a period of six months using the Poisson distribution formula:
P(X ≤ 3) = P(X=0) + P(X=1) + P(X=2) + P(X=3)
= (e^(-4)*4^0)/0! + (e^(-4)*4^1)/1! + (e^(-4)*4^2)/2! + (e^(-4)*4^3)/3!
= (0.0183 + 0.0733 + 0.1465 + 0.1953)
= 0.4334
Therefore, the probability of selling more than three combines in a period of six months is:
P(X > 3) = 1 - P(X ≤ 3)
= 1 - 0.4334
= 0.5666 or 56.66%
Therefore, the probability that the dealership will sell more than three combines in a period of six months is approximately 56.66%.