As an example, my problem is something similar to this: Lets say that you open 10 chests and each chest has a 30% chance of having an item. Calculate the confidence interval for the number of items found. 95% confidence, use Student t distribution if possible.

I was using the formula s(p) = sqrt(p(1-p)) for estimating the standard error of the probability p and the Student t distribution for the confidence interval.

The number of items found is I=n*p; where n is the number of chests opened (n=10) and p is the probability of the chest having an item (p=0.3).

I would need something like: if I open 10 chests, there's a 95% probability that the number of items found is between 2 and 7.

As an example, my problem is something similar to this: Lets say that you open 10 chests and each chest has a 30% chance of having an item. Calculate the confidence interval for the number of items found. 95% confidence, use Student t distribution if possible.

I was using the formula $s(p) = \sqrt{p(1-p)}$ for estimating the standard error of the probability p and the Student t distribution for the confidence interval.

The number of items found is I=n*p; where n is the number of chests opened (n=10) and p is the probability of the chest having an item (p=0.3).

I would need something like: if I open 10 chests, there's a 95% probability that the number of items found is between 2 and 7.