Advanced timed challenge: In AP Stats, this item is specifically about Sampling Distributions: sampling distribution, statistic vs parameter, sample proportion, sample mean. A researcher takes a sample of size $n=40$ from a skewed population. Why is the sampling distribution of the sample mean approximately normal? State the setup, compute carefully, and interpret the result.

Advanced timed challenge: In AP Stats, this item is specifically about Sampling Distributions: sampling distribution, statistic vs parameter, sample proportion, sample mean. Distinguish between a statistic and a parameter in a survey where 45% of 1000 sampled voters support a candidate. Extract the relevant value from the provided graph.

Advanced timed challenge: In AP Stats, this item is specifically about Sampling Distributions: sampling distribution, statistic vs parameter, sample proportion, sample mean. If the sample size $n$ is quadrupled, how does the standard deviation of the sampling distribution of $\bar{x}$ change? Base your justification on the data table provided.

Advanced timed challenge: In AP Stats, this item is specifically about Sampling Distributions: sampling distribution, statistic vs parameter, sample proportion, sample mean. An estimator $\hat{\theta}$ is said to be unbiased if: Provide a concise written explanation.

Advanced timed challenge: In AP Stats, this item is specifically about Sampling Distributions: sampling distribution, statistic vs parameter, sample proportion, sample mean. A random sample of n = 64 is taken from a population with $\sigma = 12$. Calculate the standard error of the sample mean $\bar{x}$. Extract the relevant value from the provided graph.

Advanced timed challenge: In AP Stats, this item is specifically about Sampling Distributions: sampling distribution, statistic vs parameter, sample proportion, sample mean. For a population proportion p = 0.40 and n = 100, check the Large Counts condition for the sampling distribution of $\hat{p}$. Base your justification on the data table provided.