Please answer the following question and show calculations.

From a sample of 50 day-care centers in Maryland, researchers want to know how much daycare costs. Assuming that costs are normally distributed with a population mean of $109 and standard deviation of $20.

a. Find the probability that the sample would mean a cost of $105 or less per week.

b. Find the probability that the sample would show mean costs between $102 and $106per week.