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# The distribution of the number of eggs laid by a certain species of hen during their...

The distribution of the number of eggs laid by a certain species of hen during their breeding period has a mean of 36 eggs with a standard deviation of 18.3. Suppose a group of researchers randomly samples 47 hens of this species, counts the number of eggs laid during their breeding period, and records the sample mean. They repeat this 1,000 times, and build a distribution of sample means. A) What is this distribution called? B) Would you expect the shape of this distribution to be symmetric, right skewed, or left skewed? Explain your reasoning. Left skewed, because the population distribution is left skewed. Left skewed, because according to the central limit theorem this distribution is approximately normal. Left skewed, because the population standard deviation is smaller than the population mean. Symmetric, because the population distribution is symmetric. Symmetric, because according to the central limit theorem this distribution is approximately normal. Symmetric, because the population standard deviation is smaller than the population mean. Right skewed, because the population distribution is right skewed. Right skewed, because according to the central limit theorem this distribution is approximately normal. Right skewed, because the population standard deviation is smaller than the population mean. C) Calculate the standard deviation of this distribution (i.e. the standard error). D) Suppose the researchers' budget is reduced and they are only able to collect random samples of 10 hens. The sample mean of the number of eggs is recorded, and we repeat this 1,000 times, and build a new distribution of sample means. What would be the standard error of this new distribution?

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