A gas station sells three grades of gasoline: regular, extra, and super. These a

Question

A gas station sells three grades of gasoline: regular, extra, and super. These are priced at $3.00, $3.20, and $3.40 per gallon, respectively. Suppose the sales of different grades of gasoline are independent of each other and let the average sell of regular, extra and super gasoline are 1000, 500 and 300 gallons with standard deviations 100, 80, and 50 gallons, respectively. What are the expected value of the revenue earned form this gas stations and what is the standard deviation of the revenue?

Explanation / Answer

From the given data, below table can be derived

Expected revenue earned = 3000+1600+1020 = 5620

std. dev. of revenue = sqrt (300^2 + 256^2 + 170^2) = 429.46

Type of Gasoline price/gallon mean sale std. dev. Of sale mean revenue std. dev. Revenue regular 3 1000 100 3000 300 extra 3.2 500 80 1600 256 super 3.4 300 50 1020 170

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