# The Sampling Distribution of a Sample Mean

## Sampling Distribution of the Mean

### Answers

- The mean of the sampling distribution of the mean is the mean of the
population from which the scores were sampled, in this case .

- The variance of the sampling distribution of the mean is the population
variance divided by . The population SD is , so the population
variance is .

- The standard error is the standard deviation of the population divided by the square root of . In this case,

- According to the central limit theorem, regardless of the shape of the
parent population, the sampling distribution of the mean approaches a
normal distribution as increases. In this case, a sample size of is
sufficiently large to cause the sampling distribution of the mean to
look about normal.

- Mean = , SD = , Skew = about : This problem is asking about the sampling distribution of the mean: Mean
= , SD = = = , Skew = about because the central
limit theorem states that the sampling distribution of the mean would be
about normal with a large enough .