In this exercise, we will simulate a sampling distribution for sample mean to demonstrate the properties of the sampling distribution for. We will draw random samples from a normally distributed population with aknownmean and standard deviation. Since we know the true mean and standard deviation, we will be able to compare oursampleresults to the true distribution. (In practice, when taking a random sample with real data, we will not know the true mean or standard deviation.) Lastly, we will calculate a confidence interval for the population mean using one of the random samples.

The weights of eggs produced by the hens at one local farm are approximately normally distributed with a mean of 1.95 ounces and a standard deviation of 0.37 ounces. Letrepresent the mean egg weight of 12 (one dozen) randomly-selected eggs from this local farm.

A)Explain why the sample meanfollows an approximately normal distribution.