A widely used measure of infant development is the Psychomotor Development Index (PDI).Since the PDI has been used so frequently, we have a pretty good idea of the population mean and standard deviation for scores on the PDI.The mean for scores is 100, and the standard deviation is 15.Given this, what is the probability that:

a)In a random sample of 100 infants, the mean PDI score is greater than 101.Make sure to show all work.

b)In a random sample of 100 infants, the mean PDI score is less than 98.Make sure to show all work.