Homes in a community served by a utility company annually use an expected 12,000 kilowatt-hours (kWh) of electricity. The same utility supplies natural gas to these homes, with an annual expected use of 85 thousand cubic feet (85 MCF). The homes vary in size and patterns of use, and so the use of utilities varies as well. The standard deviation of electricity use is 2,000 kWh and the SD of gas use is 15 MCF.
(a) Let the random variable X denote the electricity use of a home in kWh, and Y denote the use of natural gas in MCF. Do you think that the utility should model X and Y as independent?
(b) It makes little sense to add X and Y because these variables have different units. We can convert them both to dollars, then add the dollar amounts. If energy costs $0.09 per kilowatt-hour of electricity and $10 per thousand cubic feet of natural gas, then how much on average does a household in the community spend for utilities?
(c) If the correlation between electric use and gas use is 0.35, find the SD of the total utility bill paid by these households.
(d) Total expenditures for electricity and gas in the United States averaged $1,640 per household in 2001. Do the expenditures of the homes served by this utility seem unusually high, unusually low, or typical?