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Let X be the number of gallons of ice cream that is requested at a certain store on a hot summer day. Let us assume

Let X be the number of gallons of ice cream that is requested at a certain store on a hot summer day. Let us assume that the p.d.f. of X is:

f (x) = 12x (1000 - x)2/1012 for 0 < x < 1000, zero elsewhere.

How many gallons of ice cream should the store have on hand each of these days, so that the probability of exhausting its supply on a particular day is 0.05?

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