Multiple Answer 2 points Consider a sampling distribution for a sample mean. The distribution is well approximated by a Normal distribution with a mean of \( \mu_{\bar{x}} \) and a standard deviation of \( \sigma_{\boldsymbol{x}} \) if which of the follow is true. Select all that apply. The sample size is at least 10 when the population is not normal. It is never Normal. The population has a Normal distribution. The population mean must be at least 30 . The sample size is at least 30 when the population is not normal. The sample size is at least 100 when the population is not normal.

The sampling distribution of the sample mean is exactly Normal if the population itself is Normal. Additionally, if the population is not Normal, the Central Limit Theorem tells us that the sampling distribution is approximately Normal when the sample size is sufficiently large. A common rule of thumb is that a sample size of at least 30 is needed for the sampling distribution to be well approximated by a Normal distribution. Therefore, the correct answers are: • The population has a Normal distribution. • The sample size is at least 30 when the population is not normal. None of the other statements provided are generally true.