Finan 50.1

Let X1, X2, ... , Xn be a Bernoulli trials process with probability 0.3 for success. Let Xi = 1 if the ith outcome is a success and 0 otherwise. Find n so that P(abs(Sn/n - E(Sn/n)) >= 0.1) <=0.21, where Sn = X1 + ... Xn.



I ran across a partial solution to this problem which I have questions about.



It tells me that the sample average is Sn = (X1+...+Xn)/n. Why do they call it the sample if every value of Xi is included in the sum? I thought a sample was only some of the trials, but they are adding all of them.



Then they go on to equate mu with E[Sn] and sigma^2 with Var(An). How do I know when I can do that and when I cannot?



The partial solution ends with P(0.2<=(Sn/n)<=0.4)<=21/n. Why is Sn/n in there instead of X, and how do I solve for n now?



Thanks!



Thanks!

Finan 50.1