Water Consumption. In a 2008 paper by Abdul Shaban titled

“Water Poverty in Urban India: A Study of Major Cities”, the quantity of water consumed in Indian households has been studied. The data collected from a few houses has a normal distribution with mean 105 liters and standard deviation 69.8 liters. Let x denote liters of water consumed.

a. Sketch the distribution of the variable x.

b. Obtain the standardized version, z, of x.

c. Identify and sketch the distribution of z.

d. The percentage of houses that consume between 50 and 100 liters is equal to the area under the standard normal curve between and .

e. The percentage of houses that consume less than 100 liters is equal to the area under the standard normal curve that lies to the of .