Show using the definition of expected values for discrete random variables (Eq. 5.1) that for a discrete random variable, X, E(g(X)) = ∑g(x) p(x) where g(x) is linear. That is, show the formula is true assuming that g(x) = ax + b. You are showing that a special case of Eq. 5.2 is true; therefore, you many not use that formula in the derivation. Submission type: Submit entries below as answer to receive credit Save entries below (not submitted for credit yet)

The management of a supermarket wants to adopt a new promotional policy of giving a free gift to every customer who spends more than a certain amount per visit at this supermarket. the expectation of the management is that after this promotional policy is advertised, the expenditures for all customers at this supermarket will be normally distributed with a mean of $95 and a standard deviation of $20. if the management wants to give free gifts to at most 10% of the customers, what should the amount be above which a customer would receive a free gift?