In the past on average the Princeton MN school district has

In the past, on average, the Princeton, MN school district has cancelled classes three times each year for snow/ice. What is the probability the district will cancel 4 times next year if this is a Poisson distribution?

Solution

We are given that, in the past, on average, the Princeton, MN school district has cancelled classes three times each year for snow/ice.

Let X be the random variable that  district will cancel the classes.

X follows Poisson distribution with parameter 3.

We have to find P(X =4).

The probability mass function of X is,

P(X=x) = (e^- * ^x ) / x!

= 3

P(X=4) = (e^-3 * 3⁴ ) / 4! = (0.0498 * 81) / 4*3*2*1 = 4.0328 / 24

P(X=4) = 0.1680

The probability the district will cancel 4 times next year is 0.1680.