# Math Help - Central Limit Theorem

1. ## Central Limit Theorem

What is the probability that after 80 rolls of a die, the total sum of the upturned faces will exceed 260?

So far I have (1 - P(X1+...+X80 - 80(mean X1) <= 260)) / (std. dev.)(sqrt(80)).

Am I doing this correctly, and if so, how do I find the mean and std. deviation to put into the equation?

2. upturned faces=sum of the spots?

Then you want

$P(\sum_{i=1}^{80}X_i>260)$
I would put in a correct factor and approximate it with a normal...

$\approx P(\sum_{i=1}^{80}X_i>260.5)$

where the X's are iid from the distribution that puts 1/6 probability on {1,2,3,4,5,6}.