Given: f(x) = 1.55 Var(x) = 2.388 and standard deviation = 1.545

To retain as many of the jeopardized customers as possible, in addition to taking the usual steps to resolve the customer's complaint (such as granting a full refund), the company has authorized its customer service personnel to offer gift certificates to these customers as an incentive to buy from OCE again. For the purposes of planning, OCE assumes that each "jeopardized" customer will accept the $50 gift card if offered. It only makes sense to offer a gift card if the cost is less than the revenue expected from each card. Ideally, a jeopardized customer who accepts the $50 gift card would end up using that card to spend more than $50. Not every customer will spend just $50, of course, so OCE will need to account for the randomness involved in excess spending. By some estimates, customers tend to spend 20% more than the face value of their gift cards (National Funding, 2017)4 . 4National Funding (2017, December 13). 4 benefits to offering customers gift cards. Retrieved from www.nationalfunding.com/blog/4-benefits-to-offering-customers-gift-cards/ 6 (a) Suppose that a customer who receives a $50 gift card has a probability, p, of spending 20% or more above the gift card amount (and therefore has a probability of 1 p of spending less). The company will, for simplicity, assume that for any given gift card, either: 1). the customer spends exactly 20% above the face value of $50, or, 2). the customer spends only the face value of the gift card. Because a gift card is given to a customer "for free," if the customer spends $50 or less, the company has lost $50 on that card. Find the probability of excess spending of 20% that would allow an expected $3 profit per card. Hint: You will end up using the expected value formula, but you will treat the probability of excess spending, p, as a value to solve for. Show and/or explain your calculations. (b) OCE now wants to determine the expected profit per day using the $3 expected profit per card and the probability distribution in Table 1. Let Y be the expected profit per day. Find the mean, Y = E(Y ), and standard deviation, Y = p V (Y ) to two decimal places and explain what they tell you. Hint: write Y in terms of X. Show your work; a correct answer with no work shown is worth 0 points! Also, don't begin with the math; describe what you are about to do.