Central Limit Theorem Question

In summary, seniors at a college have a probability of one third to bring parents to graduation, with 600 seniors graduating this year. To estimate the probability of more than 650 parents attending, the Central Limit Theorem can be used by finding the variance of X, the number of parents in attendance. This can be calculated by subtracting E(X) squared from the expected value, which is also 600.
  • #1
Kalinka35
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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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  • #2
Okay, never mind I think I got it...
 

What is the Central Limit Theorem?

The Central Limit Theorem states that when independent random variables are added, their sum tends toward a normal distribution (also known as a bell-shaped curve) even if the original variables themselves are not normally distributed.

Why is the Central Limit Theorem important?

The Central Limit Theorem is important because it allows us to make inferences about a population based on a sample, even if the population is not normally distributed. This is essential in many statistical analyses and hypothesis testing.

What are the assumptions of the Central Limit Theorem?

The Central Limit Theorem assumes that the variables being added are independent, and that the sample size is large enough (typically n > 30). It also assumes that the variables have a finite mean and variance.

What is the difference between a sample mean and a population mean?

A sample mean is the average value of a subset of a population, while a population mean is the average value of the entire population. The Central Limit Theorem allows us to use the sample mean as an estimate for the population mean.

Can the Central Limit Theorem be applied to any type of data?

The Central Limit Theorem can be applied to any type of data, as long as the assumptions are met. However, it is most commonly used with data that follows a normal distribution.

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