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An appliance dealer sells three different models of upright freezers having 15.5, 17.8 and 21.3 cubic feet of storage space, respectively. Let X : the amount of storage space purchased by the next customer to buy a freezer. Suppose X has pmf ac 15.5 17.8 21.3 p(:c) 0.4 0.2 0.4 For all your answers below, round your final answers to 3 decimal places. a. Compute the following: an : S m : I: m 2 E b. If the price of a freezer having capacity X cubic feet is 23X 8.7 , what is the expected price paid by the next customer to buy a freezer? [:1 c. What is the variance of the price 23X 7 8.7 paid by the next customer? (Be careful with using rounded values in your calculations. This could result in round off error) :1 cl. Suppose that although the rated capacity of a freezer is X, the actual capacity is h(X) : X i 0.02X2 . What is the expected actual capacity of the freezer purchased by the next customer. S Let X be the damage incurred (in S) in a certain type of accident during a given year. Possible X values are $0, $1000, $5000, and $10000, with probabilities, 0.84, 0.12, 0.03, and 0.01, respectively. A particular company offers a $400 deductible policy. If the company wishes its expected profit to be $100, what premium amount should it charge? SS Suppose E(a:) : 4 and E(X(X i 1)) : 28.3. What is a. E(X2)) ? Hint. First verify that E(X(X 1)) : E(X2) E(X). C] b. V(X) = C] c. What is the general relationship among the quantities, E(X), E(X(X 1)) and V(X) ? 2 01/00 : E(X(X , 1)) , E00 + (E(X)) 0 WM : E(X(X e 1)) e 1300 e (Eur)? O V(X) : E(X(X 1)) + E(X) (E(X))2 O V(X) = E(X(X 1)) + E(X) + (E(X))2 A company that produces fine crystal knows from experience that 9% of its goblets have cosmetic flaws and must be classified as "seconds." a. Among eight randomly selected goblets, how likely is it that only one is a second? C] b. Among eight randomly selecte goblets, what is the probability that at least two are seconds? C] c. If goblets are examined one by one, what is the probability that at most seven must be selected to find six that are not seconds? C] Suppose that 40% of all students who have to buy a text for a particular course want a new copy (the successes!), whereas the other 60% want a used copy. Consider randomly selecting 16 purchasers. a) What are the mean value and standard deviation of the number who want to new copy of the book? (Round your standard deviation to two decimal places). standard deviation = [:] b) What is the probability that the number who want new copies is more than two standard deviations from the mean value? (Round your answer to 3 decimal places). [I c) The bookstore has 10 new copies and 10 used copies in stock. If 16 people come in one by one to purchase this text, what is the probability that all 16 will get the type of book they want from current stock? [Hint Let X = the number who want a new copy. For what values of X will all 16 get what they want?] (Round your answer to three decimal places.) B d) Suppose that new copies cost $110 and used copies cost $80. Assume the bookstore currently has 50 new copies and 50 used copies. What is the expected value of total revenue from the sale of the next 16 copies purchased? [Hint Let h(X) = the revenue when X of the 16 purchasers want new copies. Express this as a linear function.] E Indicate what rule of expected value you are using. A certain type of flashlight requires two type-D batteries, and the flashlight will work only if both is batteries have acceptable voltages. Suppose that 89% of all batteries from a certain supplier have acceptable voltages. Among ten randomly selected flashlights, what is the probability that at least nine will work? What assumptions did you make? 0 We have assumed the batteries' voltage levels are disjoint. Q We have assumed here the batteries' voltage levels are dependent. Q We have assumed the batteries' voltage levels are independent. 0 We have assumed here the batteries' voltage levels are not disjoint