In the article, "A Multifactorial Intervention Program Reduces the Duration of Delirium, Length of Hospitalization, and Morality in Delirious Patients" (Journal of the American Geriatrics Society, Vol. 53, No.4, pp. 622-628), M. Lundstrom et al. investigated whether education programs for nurses improve the outcomes for their older patients. The standard deviation of the length s of hospital stay on the intervention ward is 8.3 days.
a. For the variable "length of hospital stay," determine the sample distribution of the sample mean for samples of 80 patients on the intervention ward.
b. The distribution of the length of hospital stay is right skewed. Does the invalidate your result in part (a)? Explain your answer.
c. Obtain the probability that the sampling error made in estimating the population mean length of stay of a sample of 80 patients will be at most 2 days.