Question

3 multiple choice 1 point according to the central limit theorem, if the sample size is larger than 50, the sampling distribution of the mean is negatively skewed. bimodally distributed approximately normal. positively skewed.

Explanation:

The Central Limit Theorem (CLT) states that for a large sample size (typically \(n\geq30\)), the sampling distribution of the sample mean \(\bar{X}\) is approximately normal, regardless of the shape of the population distribution. A sample size larger than 50 is well within the range where the CLT applies. Skewed (negative or positive) and bimodal distributions are not what the CLT predicts for the sampling distribution of the mean when \(n\) is large.

Answer:

approximately normal.