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The amount of regular unleaded gas purchased every week at a particular gas

The amount of regular unleaded gas purchased every week at a particular gas station follows the normal distribution with a mean of 50000 gallons and a standard deviation of 10000 gallons. The starting supply of gasoline is 74000 gallons, and there is a scheduled weekly delivery of 47000 gallons. Compute the probability that, after 11 weeks, the supply of gasoline will be below 20000 gallons.

1 Answer

The supply will be below 20000 gallons if the total gasoline purchased in these 11 weeks is more than

591000 − 20000 = 571000 gallons.

Therefore we need to find P(T > 571000)

= P(z > 571000−11(50000) √ 1110000 )

= P(z > 0.63) = 1 − 0.7357 = 0.2643
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