The yield per acre of a certain dwarf watermelon is highly dependent on the amount of rainfall that occurs during the growing season. Following standard cultivation practices, the relationship between tons per acre, \(Y\), and inches of rainfall, \(R\), is given by

\(Y=25+2 R-.05 R^{2}\) for \(R \in[0,40]\)

(a) If expected rainfall is 10 , can expected yield be equal to 60 ?

(b) If expected rainfall is 15, define an upper bound for the value of expected yield.

(c) If expected rainfall is 15, and the variance of rainfall is 5 , what is the expected value of yield?