Ship collisions in the Houston Ship Channel are rare. Suppose the number of collisions are Poisson distributed, with a mean of 1.2 collisions every four months. What is the probability of having one or less collision over a four-month period? Round you answer to 3 decimal places.

 

Answer:

It is given:

?λ=1.2?

Number of collisions are Poisson distributed

The formula for the Poisson probability mass function is

?p(x;λ)=e^−λλ^x??/x

What is the probability of having one or less collision over a four-month period?

We want to find ?P(X≤1)?

?P(X≤1)=∑i=0?P(X=i)?

For ?X=0?

?p(0;1.2)=e^−1.21.2^0/0! ?=0.3012?

For ?X=1?

?p(1;1.2)=e^−1.21.2^1/1!?=0.3614?

Then

?P(X≤1)=0.3012+0.3614?

?P(X≤1)=0.663?

The probability of having one or less collision over a four-month period is 0.663.