The number of hurricanes hitting the coast of Florida annually has a Poisson distribution with a mean of 0.8. Answer the following two questions: a) What is the probability that more than two hurricanes will hit the Florida coast in a year? b) What is the probability that exactly one hurricane will hit the coast of Florida in a year?

a)

And we can find the individual probabilities like this:

And replacing we got:

b)

Step-by-step explanation:

Let X the random variable that represent the number of hurricanes hitting the coast of Florida annualle. We know that

The probability mass function for the random variable is given by:

And f(x)=0 for other case.

For this distribution the expected value is the same parameter

Part a

For this case we want this probability:

And for this case we can use the complement rule like this:

And we can find the individual probabilities like this:

And replacing we got:

Part b

Using the probability mass function we have:

120 seems like the most sensible answer.

step-by-step explanation:

if there is only one topping on all caramel apples and there's 120 of them. then all apples should/will be covered in sprinkles. make sense?