Question

[blank] states that the sampling distribution of x is approximately normal when the sample is large.

Answer 1

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.

Answer 2

The mean of the sampling distribution is [blank] the population mean.

Answer 3

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:

\[
E(\bar{x}) = \mu
\]