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A sampling distribution is the probability distribution of a statistic obtained from a larger population. It describes how the sample statistic (like the sample mean or proportion) varies from sample to sample. In this context, it refers to the distribution of the proportions of yellow pods obtained from repeated random samples of the pea population.

The mean of the sampling distribution, also known as the expected value, is the average of all possible sample means or proportions. According to the Central Limit Theorem, this mean will equal the population mean or proportion when the sample size is sufficiently large, regardless of the population's distribution. In this case, it questions whether the mean of the sampling distribution of proportions matches the population proportion of yellow pods.

The Law of Large Numbers states that as the size of a sample increases, the sample mean will get closer to the population mean. This principle underpins the idea that the mean of the sampling distribution of proportions will converge to the true population proportion as more samples are taken. It emphasizes the reliability of sample statistics in estimating population parameters when the sample size is large.