Central Limit Theorem Application

A die is continuously rolled 65 -1 times. What is the probability that the total sum of all rolls does not exceed 225?

I know that the expected value for each roll is 7/2 so this means that the mean sum of all the rolls would be 64*(7/2) = 224.

Also, the variance for each roll is 35/12. How do I use this to find the std deviation in all the rolls?

Re: Central Limit Theorem Application

The variance of the sum is $\displaystyle n\sigma^2$ where $\displaystyle \sigma^2$ is the variance of 1 roll.

However to apply the central limit theorum you should be thinking about the properties of the sample **mean**. if the total does not exceed 225, what can you say about the sample mean?