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 250 gallons and a standard deviation of 100 gallons. Goop sells the polymer for $25 per gallon. Goop purchases raw material for $10 per gallon and must spend $5 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. If a part of the question specifies whether to use Table 13.4, or to use Excel, then credit for a correct answer will depend on using the specified method. a. How many gallons should Goop purchase to maximize its expected profit? Use Table 13.4. b. Suppose Goop purchases 150 gallons of raw material. What is the probability that it will run out of raw material? (Round your answer to 4 decimal places.) Suppose Goop purchases 300 gallons of raw material. What are the expected sales (in C. gallons)? Use Table 13.4. d. (Round your answer to 2 decimal places.) Suppose Goop purchases 400 gallons of raw material. How much should it expect to spend on disposal costs (in dollars)? Use Table 13.4. (Round your answer to 2 decimal places.) Suppose Goop wants to ensure that there is a 92 percent probability that it will be able to e. satisfy its customers' entire demand. How many gallons of the raw material should it purchase? Use Table 13.4. Function Z -4.0 F(z) .0000 1(z) .0000 -3.9 .0000 .0000 -3.8 .0001 .0000 -3.7 .0001 .0000 -3.6 .0002 .0000 -3:5 .0002 .0001 -3.4 .0003 .0001 -3.3 .0005 .0001 -3.2 .0007 .0002 .0003 -3.1 .0010 .0004 -3.0 .0013 .0005 -2.9 .0019 .0008 .0026 -2.8 .0011 .0035 -2.7 .0015 .0047 -2.6 3 " -2.5 .0062 .0020 -2.4 .0082 .0027 -2.3 .0107 .0037 -2.2 .0139 .0049 -2.1 .0179 .0065 -2.0 .0228 .0085 -1.9 .0287 .0111 -1.8 .0359 .0143 -1.7 .0446 .0183 -1.6 .0548 .0232 .0293 -1.5 .0668 .0367 -1.4 .0808 .0455 .0968 -1.3 .0561 1151 -1.2 .0686 .1357 -1.1 .0833 1587 -1.0 1004 .1841 -0.9 1229 3440 30F Su -0.5 .3085 1978 -0.4 .3446 .2304 -0.3 .3821 .2668 -0.2 .4207 .3069 -0.1 .4602 .3509 .0 .5000 .3989 .1 .5398 .4509 .2 .5793 .5069 .5668 3 .6179 .6304 .4 .6554 .6978 .5 .6915 .7687 .7257 .6 .8429 .7580 7 .9202 .7881 8 1.0004 .8159 .9 1.0833 .8413 1.0 1.1686 .8643 1.1 1.2 1.2561 8849 O 30F Sunny com/Media/Connect Production/bne/om/Cachon_2e_OM/Table 13.4.jpg 1.3 .9032 1.3455 1.4 .9192 1.4367 1.5 .9332 1.5293 1.6 .9452 1.6232 1.7 .9554 1.7183 1.8 .9641 1.8143 1.9 .9713 1.9111 2.0 .9772 2.0085 2.1 .9821 2.1065 2.2 .9861 2.2049 2.3037 2.3 .9893 2.4027 .9918 2.4 2.5020 .9938 2.5 2.6015 .9953 2.6 2.7011 .9965 2.7 2.8008 .9974 2.8 2.9005 9981 2.9 20004 9097 20 W 30F Sunny Media/Connect Production/bne/om/Cachon_2e_OM/Table 13.4.jpg 1.3 .9032 1.3455 1.4 .9192 1.4367 1.5 .9332 1.5293 1.6 .9452 1.6232 1.7 .9554 1.7183 1.8 .9641 1.8143 1.9 .9713 1.9111 2.0 .9772 2.0085 2.1 .9821 2.1065 2.2049 2.2 .9861 2.3037 2.3 .9893 2.4027 .9918 2.4 2.5020 .9938 2.5 2.6015 .9953 2.6 2.7011 .9965 2.7 2.8008 9974 2.8 2.9005 9981 2.9 20004 0097 30F Sunny com/Media/Connect Production/bhe/om/ ble_15.4.jpg 2.4 .9918 2.4027 2.5 .9938 2.5020 2.6 .9953 2.6015 2.7 .9965 2.7011 2.8 .9974 2.8008 2.9 .9981 2.9005 3.0 .9987 3.0004 3.1 .9990 3.1003 3:2 .9993 3.2002 3.3001 3.3 .9995 3.4 .9997 3.4001 3.5001 .9998 3.5 3.6000 .9998 3.6 3.7000 .9999 3.7 3.8000 .9999 3.8 3.9000 1.0000 3.9 4.0000 1,0000 4.0 30F Sunny