Question: Sales Let \(x\) represent the amount of frozen yogurt in hundreds of gallons) sold by the G&T restaurant on any day during the summer. Storage limitations dictate that the maximum amount of frozen yogurt that can be kept at G&T on any given day is 250 gallons. Records of past sales indicate that the probability density function for \(x\) is approximated by

\(y(x)=0.32 x\) for \(0 \leq x \leq 2.5\).

1. What is the probability that on some summer day, G\&T will sell less than 100 gallons of frozen yogurt?
2. What is the mean number of gallons of frozen yogurt that G8eT expects to sell on a summer day?
3. Sketch a graph of \(y\), and locate the mean on the graph. Also, shade the region that the answer to part \(a\) represents.

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