Business statistics

The average full­sized front­loading Energy Star clothes washer uses 15 gallons of water per load (greenbuildingadvisor.com, December 4, 2015). Assume that the popula­ tion 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 full­sized front­ loading Energy Star clothes washer will provide a sample mean gallons of water used that is within one­half gallon of the population mean of 15 gallons? b. What is the probability that a random sample of 50 loads washed in a full­sized front­ loading Energy Star clothes washer will provide a sample mean gallons of water used that is at least three­quarters 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 full­sized front­ loading Energy Star clothes washer will provide a sample mean gallons of water used that is no more than one­quarter of a gallon less than the population mean of 15 gallons?