Central Limit Theorem Question

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The discussion revolves around applying the Central Limit Theorem (CLT) to estimate the probability of more than 650 parents attending a graduation ceremony for 600 seniors, given specific attendance patterns. The user defines X as the total number of parents attending, calculated from individual contributions from each student. They express confusion about determining the variance of X, particularly in calculating E(X^2). The user ultimately indicates they may have resolved their confusion. The conversation highlights the application of statistical principles in a practical scenario.
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Homework Statement


On average one third of seniors at a college will be bring parents to the graduation, one third will bring one parent and the remaining third will not bring any parents. Suppose there are 600 seniors graduating this year. Estimate the probability that more than 650 parents will attend the graduation.

Homework Equations


The Central Limit Theorem


The Attempt at a Solution


I let X = the number of parents in attendance and Xi = the number of parents brought by student i. So X = X1+...+X600.
I found that E(X)=600 and in order to use the Central Limit Theorem I need to know the variance of X, but this is what is tripping me up.
Var(X) = E(X2) - (E(X))2 but I don't know how to find (E(X))2. Is there an entirely different approach that I'm missing?
 
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Okay, never mind I think I got it...
 

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