The Central Limit Theorem (CLT) states that the sampling distribution of the sample mean (\( \bar{x} \)) is approximately normal when the sample size is large, regardless of the shape of the population distribution. Typically, a sample size of 30 or more is considered large enough for the CLT to hold.
[blank] states that the sampling distribution of x is approximately normal when the sample is large.
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The mean of the sampling distribution is [blank] the population mean.
The mean of the sampling distribution is equal to the population mean. This is a key property of the sampling distribution of the sample mean, which states that the expected value (or mean) of the sampling distribution of the sample mean (\( \bar{x} \)) is the same as the population mean (\( \mu \)). In mathematical terms, this can be expressed as:
\[ E(\bar{x}) = \mu \]
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