The average full-sized front-loading Energy Star clothes washer uses 15 gallons of water per load (greenbuildingadvisor.com, December 4, 2015). Assume that the population standard deviation for the number of gallons of water used to wash a load by these machines is 3.0.
a. What is the probability that a random sample of 90 loads washed in a full-sized frontloading Energy Star clothes washer will provide a sample mean gallons of water used that is within one-half gallon of the population mean of 15 gallons?
b. What is the probability that a random sample of 50 loads washed in a full-sized frontloading Energy Star clothes washer will provide a sample mean gallons of water used that is at least three-quarters of a gallon greater than the population mean of 15 gallons?
c. What is the probability that a random sample of 75 loads washed in a full-sized frontloading Energy Star clothes washer will provide a sample mean gallons of water used that is no more than one-quarter of a gallon less than the population mean of 15 gallons?