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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. how many gallons should the weekly delivery be so that after 11 weeks the probability that the supply is below 20000 gallons is only 0.5%?

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sqdancefan
The standard deviation of the 11-week average usage will be 10,000/√11, so the 11 week average will have a probability of 0.995 of being 57766.41757 or less. That is, total usage will have less than 0.5% probability of exceeding
.. 11 * 57766.41757 = 635430.5932 . . . gallons

We want to choose a delivery such that
.. 74000 +11*delivery -635430.5932 ≥ 20000
.. delivery ≥ (20000 -74000 +635430.6)/11 = 52857 . . . gallons