Poisson distribution for insurance

[RAYINDASKY]

Homework Statement

An insurer uses the Poisson distribution with mean 4 as the model for the number
of warranty claims per month on a particular product. Each warranty claim results
in a payment of 2 by the insurer. Find the probability that the total payment by
the insurer in a given month is less than two standard deviations above the average
monthly payment.

Homework Equations

The Attempt at a Solution

So, mean = 4
Standard deviation = 2
x=2

Will I use the density function to solve this?

 

[LCKurtz]

Homework Statement

An insurer uses the Poisson distribution with mean 4 as the model for the number
of warranty claims per month on a particular product. Each warranty claim results
in a payment of 2 by the insurer. Find the probability that the total payment by
the insurer in a given month is less than two standard deviations above the average
monthly payment.


So, mean = 4
Standard deviation = 2
x=2

Will I use the density function to solve this?

Mean of what is 2? Standard deviation of what is 2? Where did the 2 come from?

You need to define your variables to get started. If X is the number of warranty claims in a month then the mean of X is 4. What is the std deviation of X? If Y is the amount paid in claims in a month, then isn't Y = 2X? Y and X aren't the same thing. Can you get the mean and std deviation of Y? Can you get going from this?