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Central Limit Theorem for Proportions
The Central Limit Theorem for Proportions states that the distribution of sample proportions will be approximately normal, regardless of the underlying distribution of the population from which the samples are drawn.
Central Limit Theorem Definition
The Central Limit Theorem is a theorem that states that the sum of a large number of independent and identically distributed random variables will be approximately normally distributed.
Central Limit Theorem Statistics Example
The Central Limit Theorem states that the sampling distribution of a statistic will be normally distributed, regardless of the distribution of the population from which the sample was drawn, as long as the sample size is large enough.
To illustrate the Central Limit Theorem, we will use an example. Suppose we want to know the average weight of all college students on campus. We could take a random sample of 100 students and calculate the average weight for that sample. We would then expect the average weight for the entire population of college students to be close to the average weight for our sample.
The Central Limit Theorem tells us that the average weight for the entire population of college students will be normally distributed, regardless of the distribution of weights for individual students. This is because the Central Limit Theorem applies to the sampling distribution of a statistic, not the distribution of the population. As long as our sample size is large enough, the sampling distribution of the average weight for college students will be normal.
Central Limit Theorem Formula
The Central Limit Theorem (CLT) states that given a sufficiently large sample size, the sampling distribution of the sample mean will be approximately normal.
