Question: Suppose the amount of heating oil used annually by households in Iowa is normally distributed with a mean of 318 gallons per household per year and a standard deviation of 62 gallons of heating oil per household per year. What is the probability that a randomly selected Iowa household uses more than 260 gallons of heating oil per year?

1. What is the probability that a randomly selected Iowa household uses between 190 and 310 gallons per year?
2. If the members of a particular household were scared into using fuel conservation measures by newspaper accounts of the probable price of heating oil next year, and they decided they wanted to use less oil than 95% of all other Iowa households currently using heating oil, what is the maximum amount of oil they can use and still accomplish their conservation objective?

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