. (20 points) Goop Inc. needs to order a raw material to make a special polymer. The demand for the polymer is forecasted to be normally distributed with a mean of 300 gallons and a standard deviation of 100 gallons. Goop sells the polymer for $28 per gallon. Goop purchases raw material for $13 per gallon and must spend $2 per gallon to dispose of all unused raw material due to government regulations. (One gallon of raw material yields one gallon of polymer.) If demand is more than Goop can make, then Goop sells only what it has made and the rest of the demand is lost. Use Table 13.4. a. How many gallons should Goop purchase to maximize its expected profit? Use Table 13.4. (Round your answer to 4 decimal places. Enter your answer a whole number.) b. Suppose Goop purchases 170 gallons of raw material. What is the probability that it will run out of raw material? (Round your answer to 2 decimal places.) c. Suppose Goop purchases 350 gallons of raw material. What are the expected sales (in gallons)? Use Table 13.4 and the round-up rule. (Round your answer to 2 decimal places.) d. Suppose Goop purchases 450 gallons of raw material. How much should it expect to spend on disposal costs (in dollars)? Use Table 3.14 and the round- up rule. (Round your answer to 2 decimal places.) Fiz) F(x) 7(2) .0000 10000 -1.3 .0968 0455 3.9 0000 0000 -12 1151 0561 -3.8 0001 0000 -1.1 1357 0686 -3.7 .0001 0000 -1,0 1587 0883 -3.6 0002 0000 -0.9 1841 1004 -3.5 0002 0001 -0.8 2119 1202 -3.4 0003 0001 --0.7 .2420 1429 -3.3 .0005 0001 -0.6 2743 . 1687 -3.2 0007 0002 -0.5 3085 .1978 0010 .0003 -0.4 3446 2304 -3.0 20013 .0004 -0.8 13821 2668 29 0019 .0005 -0.2 4207 3069 -2.8 .0026 0008 -0.1 3509 4602 -2.7 0035 .5000 0011 3989 0047 0015 .5398 -2.6 4509 20062 0020 2 2.5 -5793 5069 0082 .0027 13 -2.4 6179 5668 4 10037 6554 -2.3 6304 .0107 -2.2. 6978 0139 0049 .6915 7 257 7687 0179 .0065 7580 8429 -2.0 0228 0085 0287 9202 0111 7881 .8159 1.0004 9 -1.8 0359 0143 -1.7 .8413 1.0833 0446 0183 1.0 .8643 1.1686 0232 0548 1.2 8849 1.2561 -1.5 0293 0668 1.8 9082 1.3455 -1.4 0367 0808 Fz) () I(z) Z F[z) .9192 1.4367 0968 0455 1.5 0561 .9332 1.5293 .1151 0686 1.6 .9452 1357 1.6232 .9554 1.7183 1587 0833 1.8 .9641 1.8143 -0.9 . 1841 . 1004 1.9111 -0.8 2119 9713 .1202 .1429 2.0 9772 .2420 2.0085 -0.6 2743 1687 2.1 9821 2.1065 -0.5 3085 .1978 22 .9861 2.2049 .3446 12304 2.B -0.4 .9893 2.3037 -0.3 .3821 .2668 2.4 9918 2.4027 -0.2 4207 .3069 2.5 .9938 2.5020 -0.1 4602 .3509 2.6 .9953 2.6015 .5000 .3989 9965 2.7011 15398 4509 2.8 9974 2.8008 5793 5069 9981 2.9005 13 .6179 5668 3.0 .9987 3.0004 4 6554 6304 3.1 9990 3. 1003 -5 6915 6978 3.2 9993 3.2002 6 7257 7687 3.3 9995 7580 .8429 3.4 9997 3.4001 7881 .9202 3.5 9998 3.5001 9 8 159 1.0004 3.6 -9998 3.6000 8413 1.0833 37 9999 3.7000 18643 1.1686 3.8 9999 3.8000 8849 1.2561 3.9 1.0000 8.9000 1.3 9032 1.3455 4.0 1.0000 4.0000