According to the Beverage Marketing Corporation, the per capita consumption of bottled water in the United States is 2.3 gallons per month. Assume the standard deviation for this population is 0.75 gallons per month. Consider a random sample of 36 people.

a. What is the probability that the sample mean will be less than 2.1 gallons per month?

b. What is the probability that the sample mean will be more than 2.2 gallons per month?

c. Identify the symmetrical interval that includes 95% of the sample means if the true population mean is 2.3 gallons per month.