"The theorem states that: “If a variable X from a population has mean μ and finite variance σ2, then the sampling distribution of the sample mean ⎯ X approaches a normal distribution with mean μ and variance σ2/n as the sample size n approaches infinity.” As n → ∞, the sampling distribution of ⎯ X approaches normality. Due to the Central Limit Theorem, the normal distribution has found a central place in the theory of statistical inference.(Since, in many situations, the sample is large enough for our sampling distribution to be approximately normal, therefore we can utilize the mathematical properties of the normal distribution to draw inferences about the variable of interest). The rule of thumb in this regard is that if the sample size, n, is greater than or equal to 30, then we can assume that the sampling distribution of ⎯ X is approximately normally distributed. On the other hand, If the POPULATION sampled is normally distributed, then the sampling distribution of ⎯ X will also be normal regardless of sample size. In other words, ⎯ X will be normally distributed with mean μ and variance σ2/n. Source: http://in.docsity.com/en-docs/T_Distribution-Statistics-Solved_Quizes_"
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