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