SOLUTION: The amount of gas a local gas station sells is random. The following describes the distribution of gasoline sales in a given day. There is a probability of 0.18 that the gas statio

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Question 1205490: The amount of gas a local gas station sells is random. The following describes the distribution of gasoline sales in a given day. There is a probability of 0.18 that the gas station will sell 1100 gallons of gas; probability of 0.20 that the gas station will sell 1400 gallons of gas; probability of 0.34 that the gas station will sell 1600 gallons of gas. Otherwise, the station sells 2100 gallons of gas. What is the expected number of gallons the station sells in a day?
Answer by math_tutor2020(3816) About Me  (Show Source):
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x = number of gallons of gas sold in a day
XP(X)X*P(X)
11000.18198
14000.20280
16000.34544
21000.28588

The 0.28 at the bottom of the P(X) column is due to the calculation 1 - (0.18+0.20+0.34)
Each P(x) value must be between 0 and 1, and all of those probability values add to 1.

Add up each item in the X*P(X) column:
198+280+544+588 = 1610 is the expected number of gallons sold in a day.