Solving P(11<M<12) Using CLT and Standard Normal Distribution CDF

[kingwinner]

Homework Statement

Let M=(X₁+X₂+...+X₁₀₀)/100 where each X_i's has the same distribution of X. Find P(11<M<12) in terms of the cumulative distribution function for the standard normal distribution.

Homework Equations

The Attempt at a Solution

This looks like a "central limit theorem(CLT)" question to me, but with a careful look at the assumptions of CLT, it says that the X_i's must be independent and identically distributed while in this question, there is nothing that indicates independence. How can I solve this problem then?



Thank you for helping!

 

[kingwinner]

Any stat guy here? Please help...

 

[Avodyne]

Well, the problem says that each X_i has "the same distribution", and I would say that implies that this distribution must be independent of the other X_i's. But we don't even need to worry about this, because the problem goes on to tell us to use the normal distribution, which is what the CLT would tell us to do.