Central Limit Theorem Question

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SUMMARY

The discussion centers on applying the Central Limit Theorem (CLT) to estimate the probability of more than 650 parents attending a college graduation with 600 seniors. The average distribution indicates that one third of seniors will bring parents, leading to an expected attendance of 600 parents. The user initially struggled with calculating the variance of the total number of parents but later indicated a resolution to their confusion regarding the expected value calculations.

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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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