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![**Probability Distribution of Freezer Storage Space**
An appliance dealer sells three different models of upright freezers with storage capacities of 13.5, 15.9, and 19.1 cubic feet, respectively. Let \( X \) represent the storage space purchased by the next customer. The probability distribution of \( X \) is as follows:
\[
\begin{array}{c|ccc}
x & 13.5 & 15.9 & 19.1 \\
\hline
f(x) & 0.2 & 0.4 & 0.4 \\
\end{array}
\]
(a) If the price of a freezer with \( X \) cubic feet is \( 25X - 8.5 \), what is the expected price paid by the next customer to buy a freezer?
(b) Suppose that although the rated capacity of a freezer is \( X \), the actual capacity is given by \( h(X) = X - 0.01X^2 \). What is the expected actual capacity of the freezer purchased by the next customer?](https://content.bartleby.com/qna-images/question/80864b91-d3a3-4910-ac0e-8d4cb607fd82/21ca9731-b728-43f3-ae7c-4b516bfa42f6/w5ktotw_processed.jpeg)
