The correct answer is: A. Central Limit Theorem
The Central Limit Theorem (CLT) states that, given a sufficiently large sample size, the sampling distribution of the arithmetic mean of a variable will be approximately normally distributed, regardless of the underlying distribution of the variable.
The CLT is a powerful tool that can be used to make inferences about a population based on a sample. For example, if we know that the average height of a population is 6 feet, and we take a sample of 100 people from that population, we can use the CLT to estimate the probability that the average height of the sample is greater than 6 feet 2 inches.
The CLT is based on the following assumptions:
- The population is normally distributed.
- The sample is randomly selected from the population.
- The sample size is large enough.
The CLT is a powerful tool, but it is important to remember that it is only an approximation. The actual distribution of the sample mean may not be exactly normal, especially if the sample size is small. However, the CLT becomes more accurate as the sample size increases.
The Central Mean Theorem (CMT) is a special case of the CLT. The CMT states that, given a sufficiently large sample size, the sampling distribution of the mean of a variable will be normally distributed, regardless of the underlying distribution of the variable, as long as the variable has a finite mean and variance.
The Centroid Limit Theorem (CLT) is a generalization of the CLT. The CLT states that, given a sufficiently large sample size, the sampling distribution of the centroid of a variable will be normally distributed, regardless of the underlying distribution of the variable, as long as the variable has a finite mean and variance.
The CLT, CMT, and CLT are all important theorems in statistics. They can be used to make inferences about a population based on a sample.