The Distribution. FQ$),$ and Expected Inventory. NQ$).$ Functions for the Standard Normal Distribution FunctionGoop Incorporated 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 $200$ gallons and a standard deviation of $100$ gallons. Goop sells the polymer for $$26$ per gallon. Goop purchases raw material for $$8$ per gallon and must spend $$10$ 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 $13\mathrm{.}4.$

Note: If a part of the question specifies whether to use Table $13\mathrm{.}4,$ or to use Excel, then credit for a correct answer will depend on using the specified method.

How many gallons should Goop purchase to maximize its expected profit? Use Table $13\mathrm{.}4.$

Note: Enter your answer as a whole number.

Suppose Goop purchases $120$ gallons of raw material. What is the probability that it will run out of raw material? Use Table $13\mathrm{.}4.$

Note: Round your answer to $4$ decimal places.

Suppose Goop purchases $300$ gallons of raw material. What are the expected sales $($in gallons$)?$ Use Table $13\mathrm{.}4$ and the round$-$up rule.

Note: 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 $13\mathrm{.}4$ and the round$-$up rule.

Note: 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 satisfy its customers$’$ entire demand. How many gallons of the raw material should it purchase? Use Table $13\mathrm{.}4$ and the round$-$up rule.

Note: Enter your answer as a whole number.

 

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Z F(z) K(z) TABLE 13.4 The Distribution, F(Q), and Expected Inventory. (Q), Functions for the Standard Normal Distribution Function 1(z) F(z) (2) F(z) -4.0 .0000 .0000 -1.3 .0968 .0455 1.4 .9192 -3.9 .0000 .0000 -1.2 .1151 .0561 1.5 .9332 1.4367 1.5293 -3.8 .0001 .0000 -1.1 .1357 .0686 1.6 .9452 1.6232 -3.7 .0001 .0000 -1.0 .1587 .0833 1.7 .9554 1.7 183 -3.6 .0002 .0000 -0.9 1841 .1004 1.8 .9641 1.8143 -3.5 .0002 .0001 -0.8 2119 1202 1.9 9713 1.9111 -3.4 .0003 .0001 -0.7 .2420 1429 2.0 .9772 2.0085 -3.3 .0005 .0001 -0.6 .2743 1687 2.1 .9821 2.1065 -3.2 .0007 .0002 -0.5 .3085 .1978 2.2 .9861 2.2049 -3.1 .0010 .0003 -0.4 .3446 .2304 2.3 .9893 2.3037 -3.0 .0013 .0004 -0.3 .3821 .2668 2.4 9918 2.4027 -2.9 .0019 .0005 -0.2 .4207 .3069 2.5 .9938 2.5020 -2.8 .0026 .0008 -0.1 .4602 .3509 2.6 .9953 2.6015 -2.7 .0035 .0011 .0 .5000 .3989 2.7 .9965 2.7011 -2.6 .0047 .0015 1 .5398 .4509 2.8 .9974 2.8008 -2.5 .0062 .0020 .2 .5793 .5069 2.9 9981 2.9005 -2.4 .0082 .0027 3 .6179 .5668 3.0 .9987 3.0004 -2.3 .0107 .0037 4 .6554 .6304 3.1 9990 3.1003 -2.2 .0139 .0049 .5 .6915 .6978 3.2 9993 3.2002 -2.1 0179 .0065 .6 .7257 .7687 3.3 .9995 3.3001 -2.0 .0228 .0085 .7 .7580 .8429 3.4 .9997 3.4001 -1.9 .0287 .0111 .8 .7881 .9202 3.5 9998 3.5001 -1.8 .0359 0143 .9 .8159 1.0004 3.6 9998 3.6000 -1.7 .0446 .0183 1.0 .8413 1.0833 3.7 9999 3.7000 -1.6 .0548 .0232 1.1 .8643 1.1686 3.8 9999 3.8000 -1.5 .0668 .0293 1.2 .8849 1.2561 3.9 1.0000 3.9000 -1.4 .0808 .0367 1.3 .9032 1.3455 4.0 1.0000 4.0000 Z F(z) K(z) TABLE 13.4 The Distribution, F(Q), and Expected Inventory. (Q), Functions for the Standard Normal Distribution Function 1(z) F(z) (2) F(z) -4.0 .0000 .0000 -1.3 .0968 .0455 1.4 .9192 -3.9 .0000 .0000 -1.2 .1151 .0561 1.5 .9332 1.4367 1.5293 -3.8 .0001 .0000 -1.1 .1357 .0686 1.6 .9452 1.6232 -3.7 .0001 .0000 -1.0 .1587 .0833 1.7 .9554 1.7 183 -3.6 .0002 .0000 -0.9 1841 .1004 1.8 .9641 1.8143 -3.5 .0002 .0001 -0.8 2119 1202 1.9 9713 1.9111 -3.4 .0003 .0001 -0.7 .2420 1429 2.0 .9772 2.0085 -3.3 .0005 .0001 -0.6 .2743 1687 2.1 .9821 2.1065 -3.2 .0007 .0002 -0.5 .3085 .1978 2.2 .9861 2.2049 -3.1 .0010 .0003 -0.4 .3446 .2304 2.3 .9893 2.3037 -3.0 .0013 .0004 -0.3 .3821 .2668 2.4 9918 2.4027 -2.9 .0019 .0005 -0.2 .4207 .3069 2.5 .9938 2.5020 -2.8 .0026 .0008 -0.1 .4602 .3509 2.6 .9953 2.6015 -2.7 .0035 .0011 .0 .5000 .3989 2.7 .9965 2.7011 -2.6 .0047 .0015 1 .5398 .4509 2.8 .9974 2.8008 -2.5 .0062 .0020 .2 .5793 .5069 2.9 9981 2.9005 -2.4 .0082 .0027 3 .6179 .5668 3.0 .9987 3.0004 -2.3 .0107 .0037 4 .6554 .6304 3.1 9990 3.1003 -2.2 .0139 .0049 .5 .6915 .6978 3.2 9993 3.2002 -2.1 0179 .0065 .6 .7257 .7687 3.3 .9995 3.3001 -2.0 .0228 .0085 .7 .7580 .8429 3.4 .9997 3.4001 -1.9 .0287 .0111 .8 .7881 .9202 3.5 9998 3.5001 -1.8 .0359 0143 .9 .8159 1.0004 3.6 9998 3.6000 -1.7 .0446 .0183 1.0 .8413 1.0833 3.7 9999 3.7000 -1.6 .0548 .0232 1.1 .8643 1.1686 3.8 9999 3.8000 -1.5 .0668 .0293 1.2 .8849 1.2561 3.9 1.0000 3.9000 -1.4 .0808 .0367 1.3 .9032 1.3455 4.0 1.0000 4.0000

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