In a study to observe the levels of Vitamin D in newborns and their mothers, a random sample of 125 newborns was tested and 72 were declared to be deficient in Vitamin D.

Explain why we can apply the Central Limit Theorem to make inferences from this sample and then find an 88% confidence interval for the proportion of all newborns that are Vitamin D deficient. In a subsequent study, 288 of 500 randomly selected newborns were found to be Vitamin D deficient. Use the results from this new study to find a confidence interval at the same confidence level.