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{"sheet":"NormalCurve","index":0,"n_rows":77,"n_cols":5,"rows_kept":77,"cut":false,"hidden":false,"merged":[]}
["Normal Curve"]
["Unit Normal"]
[0,"mean"]
[1,"standard deviation"]
[0.1,"graph increment"]
[null,"# SDs","Probability","Probability","Cum Prob"]
[1,-3.5,{"$f":"EXP(-((B7-$A$3)^2)/(2*$A$4^2))/($A$4*(2*PI())^0.5)","v":8.7268269504576015E-4},{"$f":"_xlfn.NORM.DIST(B7,$A$3,$A$4,0)","v":8.7268269504576015E-4},{"$f":"_xlfn.NORM.DIST(B7,$A$3,$A$4,1)","v":2.3262907903552504E-4}]
[{"$f":"1+A7","v":2},{"$f":"B7+$A$5","v":-3.4},{"$f":"EXP(-((B8-$A$3)^2)/(2*$A$4^2))/($A$4*(2*PI())^0.5)","v":1.2322191684730199E-3},{"$f":"_xlfn.NORM.DIST(B8,$A$3,$A$4,0)","v":1.2322191684730199E-3},{"$f":"_xlfn.NORM.DIST(B8,$A$3,$A$4,1)","v":3.369292656768808E-4}]
[3,{"$f":"B8+$A$5","v":-3.3},1.7225689390536812E-3,1.7225689390536812E-3,4.8342414238377744E-4]
[4,-3.1999999999999997,2.3840882014648447E-3,2.3840882014648443E-3,6.8713793791584817E-4]
[5,-3.0999999999999996,3.2668190561999247E-3,3.2668190561999247E-3,9.676032132183561E-4]
[6,-2.9999999999999996,4.4318484119380162E-3,4.4318484119380153E-3,1.3498980316300954E-3]
[7,-2.8999999999999995,5.9525324197758642E-3,5.9525324197758642E-3,1.8658133003840378E-3]
[8,-2.7999999999999994,7.915451582979979E-3,7.9154515829799772E-3,2.5551303304279364E-3]
[9,-2.6999999999999993,1.0420934814422614E-2,1.0420934814422614E-2,3.4669738030406756E-3]
[10,-2.5999999999999992,1.3582969233685644E-2,1.3582969233685644E-2,4.6611880237187606E-3]
[11,-2.4999999999999991,1.7528300493568578E-2,1.7528300493568578E-2,6.2096653257761522E-3]
[12,-2.399999999999999,2.2394530294842951E-2,2.2394530294842948E-2,8.1975359245961502E-3]
[13,-2.2999999999999989,2.8327037741601249E-2,2.8327037741601249E-2,1.0724110021675828E-2]
[14,-2.1999999999999988,3.5474592846231535E-2,3.5474592846231535E-2,1.3903447513498641E-2]
[15,-2.0999999999999988,4.3983595980427309E-2,4.3983595980427309E-2,1.7864420562816605E-2]
[16,-1.9999999999999987,5.3990966513188209E-2,5.3990966513188202E-2,2.2750131948179264E-2]
[17,-1.8999999999999986,6.5615814774676776E-2,6.5615814774676776E-2,2.8716559816001873E-2]
[18,-1.7999999999999985,7.8950158300894385E-2,7.8950158300894385E-2,3.5930319112925921E-2]
[19,-1.6999999999999984,9.4049077376887197E-2,9.4049077376887197E-2,4.4565462758543187E-2]
[20,-1.5999999999999983,0.11092083467945586,0.11092083467945585,5.4799291699558182E-2]
[21,-1.4999999999999982,0.12951759566589208,0.12951759566589208,6.6807201268858279E-2]
[22,-1.3999999999999981,0.14972746563574527,0.14972746563574524,8.0756659233771302E-2]
[23,-1.299999999999998,0.17136859204780783,0.1713685920478078,9.6800484585610636E-2]
[24,-1.199999999999998,0.19418605498321342,0.19418605498321342,0.11506967022170861]
[25,-1.0999999999999979,0.21785217703255108,0.21785217703255108,0.13566606094638309]
[26,-0.99999999999999789,0.24197072451914392,0.24197072451914389,0.15865525393145755]
[27,-0.89999999999999791,0.26608524989875532,0.26608524989875532,0.18406012534676006]
[28,-0.79999999999999793,0.28969155276148328,0.28969155276148323,0.2118553985833973]
[29,-0.69999999999999796,0.31225393336676172,0.31225393336676172,0.24196365222307364]
[30,-0.59999999999999798,0.33322460289180006,0.33322460289180006,0.27425311775007422]
[31,-0.499999999999998,0.35206532676429986,0.35206532676429986,0.30853753872598755]
[32,-0.39999999999999802,0.36827014030332367,0.36827014030332361,0.34457825838967654]
[33,-0.29999999999999805,0.38138781546052436,0.38138781546052436,0.3820885778110481]
[34,-0.19999999999999804,0.3910426939754561,0.39104269397545605,0.42074029056089773]
[35,-9.9999999999998035E-2,0.39695254747701192,0.39695254747701186,0.46017216272297179]
[36,1.9706458687096529E-15,0.3989422804014327,0.3989422804014327,0.50000000000000078]
[37,0.10000000000000198,0.3969525474770117,0.3969525474770117,0.53982783727702977]
[38,0.20000000000000198,0.39104269397545577,0.39104269397545577,0.57925970943910388]
[39,0.30000000000000199,0.38138781546052386,0.38138781546052386,0.61791142218895345]
[40,0.40000000000000202,0.36827014030332306,0.36827014030332306,0.65542174161032496]
[41,0.500000000000002,0.35206532676429919,0.35206532676429919,0.6914624612740139]
[42,0.60000000000000198,0.33322460289179928,0.33322460289179923,0.72574688224992712]
[43,0.70000000000000195,0.31225393336676088,0.31225393336676088,0.75803634777692763]
[44,0.80000000000000193,0.28969155276148234,0.28969155276148234,0.78814460141660381]
[45,0.90000000000000191,0.26608524989875437,0.26608524989875437,0.81593987465324103]
[46,1.000000000000002,0.24197072451914289,0.24197072451914287,0.84134474606854348]
[47,1.1000000000000021,0.21785217703255005,0.21785217703255005,0.86433393905361777]
[48,1.2000000000000022,0.19418605498321245,0.19418605498321242,0.88493032977829222]
[49,1.3000000000000023,0.17136859204780686,0.17136859204780686,0.90319951541439003]
[50,1.4000000000000024,0.14972746563574438,0.14972746563574438,0.91924334076622927]
[51,1.5000000000000024,0.12951759566589127,0.12951759566589127,0.93319279873114225]
[52,1.6000000000000025,0.11092083467945513,0.11092083467945513,0.94520070830044234]
[53,1.7000000000000026,9.4049077376886503E-2,9.4049077376886503E-2,0.95543453724145722]
[54,1.8000000000000027,7.8950158300893788E-2,7.8950158300893788E-2,0.96406968088707445]
[55,1.9000000000000028,6.5615814774676262E-2,6.5615814774676248E-2,0.97128344018399837]
[56,2.0000000000000027,5.3990966513187771E-2,5.3990966513187771E-2,0.9772498680518209]
[57,2.1000000000000028,4.3983595980426941E-2,4.3983595980426941E-2,0.98213557943718355]
[58,2.2000000000000028,3.5474592846231223E-2,3.5474592846231216E-2,0.98609655248650152]
[59,2.3000000000000029,2.8327037741600985E-2,2.8327037741600981E-2,0.98927588997832427]
[60,2.400000000000003,2.2394530294842733E-2,2.2394530294842729E-2,0.99180246407540396]
[61,2.5000000000000031,1.7528300493568398E-2,1.7528300493568398E-2,0.99379033467422395]
[62,2.6000000000000032,1.3582969233685507E-2,1.3582969233685505E-2,0.99533881197628127]
[63,2.7000000000000033,1.0420934814422503E-2,1.0420934814422501E-2,0.99653302619695938]
[64,2.8000000000000034,7.9154515829798905E-3,7.9154515829798905E-3,0.99744486966957213]
[65,2.9000000000000035,5.9525324197757957E-3,5.9525324197757957E-3,0.99813418669961596]
[{"$f":"1+A71","v":66},3.0000000000000036,{"$f":"EXP(-((B72-$A$3)^2)/(2*$A$4^2))/($A$4*(2*PI())^0.5)","v":4.4318484119379607E-3},{"$f":"_xlfn.NORM.DIST(B72,$A$3,$A$4,0)","v":4.4318484119379598E-3},{"$f":"_xlfn.NORM.DIST(B72,$A$3,$A$4,1)","v":0.9986501019683699}]
[67,{"$f":"B72+$A$5","v":3.1000000000000036},3.266819056199884E-3,3.266819056199884E-3,0.99903239678678168]
[68,3.2000000000000037,2.3840882014648148E-3,2.3840882014648148E-3,0.99931286206208414]
[69,3.3000000000000038,1.7225689390536585E-3,1.7225689390536582E-3,0.99951657585761622]
[70,3.4000000000000039,1.2322191684730024E-3,1.2322191684730024E-3,0.99966307073432314]
[71,3.500000000000004,8.7268269504574769E-4,8.7268269504574769E-4,0.99976737092096446]

{"sheet":"Normdist","index":1,"n_rows":84,"n_cols":10,"rows_kept":84,"cut":false,"hidden":false,"merged":[]}
["Normalizing a Discrete Distribution"]
["In practice a scenario forecast is often used to get a better estimate of the distribution of a quantity that"]
["is approximately normally distributed. For example, we might estimate the mean and standard"]
["deviation of next year's number of units sold (Quantity) and Return on Equity (ROE) with a scenario"]
["forecast."]
["Scenario Forecast",null,"Probability","Quantity","ROE"]
[null,"Good economy",0.35,1250,0.26997150193439684]
[null,"Average economy",0.4,1000,0.12639175118550003]
[null,"Bad economy",0.25,750,-1.718799956339679E-2]
[null,"Mean",null,{"$f":"+MMULT(TRANSPOSE($C$7:$C$9),D7:D9)","v":1025},{"$f":"+MMULT(TRANSPOSE($C$7:$C$9),E7:E9)","v":0.1407497262603897},{"$f":"getformula(E10)","v":"<--  {=+MMULT(TRANSPOSE($C$7:$C$9),E7:E9)}"},null,null,"Using MMULT to calculate Variance:"]
[null,"Variance",null,{"$f":"(D7-D$10)^2*$C7+(D8-D$10)^2*$C8+(D9-D$10)^2*$C9","v":36875},{"$f":"(E7-E$10)^2*$C7+(E8-E$10)^2*$C8+(E9-E$10)^2*$C9","v":1.2162935446818048E-2},{"$f":"getformula(E11)","v":"<--  =(E7-E$10)^2*$C7+(E8-E$10)^2*$C8+(E9-E$10)^2*$C9"},null,null,{"$f":"MMULT(TRANSPOSE(C7:C9),(D7:D9-$D$10)^2)","v":36875},{"$f":"getformula(I11)","v":"<--  =MMULT(TRANSPOSE(C7:C9),(D7:D9-$D$10)^2)"}]
[null,"Standard Deviation",null,{"$f":"SQRT(D11)","v":192.02864369671519},{"$f":"SQRT(E11)","v":0.11028569919449234},"<--  =SQRT(E11)"]
["Breakeven Points and Probability of Breakeven Using Normalized Distributions"]
[null,"Now assume that the discrete distributions of Quantity & Sales in the scenario"]
[null,"forecast are converted to normal distributions using the means and standard deviations"]
[null,"calculated above. Our goal below is to calculate the probability of breaking even for"]
[null,"both EBIT and ROE."]
[]
[null,null,null,"Breakeven Quantity (Units)",750,"<-- EBIT = 0"]
[null,null,null,"Breakeven ROE (Units)",779,"<-- ROE = 0"]
[null,null,null,"Expected ROE",{"$f":"E10","v":0.1407497262603897},"Expected Quantity",{"$f":"D10","v":1025}]
[null,null,null,"Standard Deviation of ROE",{"$f":"E12","v":0.11028569919449234},"Standard Deviation of Quantity",{"$f":"D12","v":192.02864369671519}]
[null,null,null,"P(ROE>0)",{"$f":"1-NORMDIST(0,E21,E22,1)","v":0.89906257966720138},"<-- Uses Expected ROE & Standard Deviation of ROE"]
[null,null,null,"P(EBIT>0)",{"$f":"1-NORMDIST(E19,G21,G22,1)","v":0.92393925305788538},{"$f":"getformula(E24)","v":"<--  =1-NORMDIST(E19,G21,G22,1)"},"<-- Uses Expected Quantity & Standard Deviation of Quantity"]
[null,null,null,"P(ROE>0)",{"$f":"1-NORMDIST(E20,G21,G22,1)","v":0.89991350792071656},{"$f":"getformula(E25)","v":"<--  =1-NORMDIST(E20,G21,G22,1)"},"<-- Uses Expected Quantity & Standard Deviation of Quantity"]
[]
[]
[]
[{"$f":"G21","v":1025},"mean"]
[{"$f":"G22","v":192.02864369671519},"standard deviation"]
[0.25,"graph increment"]
[null,"# SDs","X","Probability","Cum Prob"]
[1,-3.5,{"$f":"B33*$A$30+$A$29","v":352.89974706149678},{"$f":"_xlfn.NORM.DIST(C33,$A$29,$A$30,0)","v":4.5445443879927171E-6},{"$f":"_xlfn.NORM.DIST(C33,$A$29,$A$30,1)","v":2.3262907903552504E-4}]
[{"$f":"1+A33","v":2},{"$f":"B33+$A$31","v":-3.25},{"$f":"B34*$A$30+$A$29","v":400.90690798567562},{"$f":"_xlfn.NORM.DIST(C34,$A$29,$A$30,0)","v":1.0566382276304524E-5},{"$f":"_xlfn.NORM.DIST(C34,$A$29,$A$30,1)","v":5.7702504239076603E-4}]
[3,{"$f":"B34+$A$31","v":-3},448.91406890985445,2.3079100735292118E-5,1.3498980316300933E-3]
[4,-2.75,496.92122983403317,4.7355239960727764E-5,2.9797632350545521E-3]
[5,-2.5,544.928390758212,9.1279614104093035E-5,6.2096653257761331E-3]
[6,-2.25,592.93555168239084,1.6528602829584196E-4,1.2224472655044696E-2]
[7,{"$f":"B38+$A$31","v":-2},640.94271260656956,2.81161005326163E-4,2.2750131948179184E-2]
[8,-1.75,688.94987353074839,4.4929400721475477E-4,4.00591568638171E-2]
[9,-1.5,736.95703445492722,6.7447018930388478E-4,6.6807201268858057E-2]
[10,-1.25,784.96419537910606,9.5115542073761128E-4,0.10564977366685525]
[11,-1,832.97135630328478,1.2600762045755281E-3,0.15865525393145699]
[12,-0.75,880.97851722746361,1.5681901739118291E-3,0.22662735237686821]
[13,-0.5,928.98567815164245,1.8334000594220823E-3,0.30853753872598699]
[14,-0.25,976.99283907582117,2.0135960415027577E-3,0.40129367431707619]
[15,0,1025,2.0775144411867598E-3,0.5]
[16,0.25,1073.0071609241788,2.0135960415027577E-3,0.59870632568292381]
[17,0.5,1121.0143218483577,1.8334000594220821E-3,0.69146246127401323]
[18,0.75,1169.0214827725363,1.5681901739118297E-3,0.77337264762313163]
[19,1,1217.0286436967151,1.260076204575529E-3,0.84134474606854293]
[20,1.25,1265.0358046208939,9.5115542073761128E-4,0.89435022633314476]
[21,1.5,1313.0429655450728,6.7447018930388478E-4,0.93319279873114191]
[22,1.75,1361.0501264692516,4.4929400721475477E-4,0.95994084313618289]
[23,2,1409.0572873934304,2.81161005326163E-4,0.97724986805182079]
[24,2.25,1457.0644483176093,1.652860282958418E-4,0.98777552734495533]
[25,2.5,1505.0716092417879,9.1279614104093103E-5,0.99379033467422384]
[26,2.75,1553.0787701659669,4.7355239960727703E-5,0.99702023676494544]
[27,3,1601.0859310901456,2.3079100735292118E-5,0.9986501019683699]
[28,3.25,1649.0930920143244,1.0566382276304524E-5,0.99942297495760923]
[29,3.5,1697.1002529385032,4.5445443879927171E-6,0.99976737092096446]
[]
[]
["Data for Vertical chart lines marking standard deviations from mean."]
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[null,-3,{"$f":"B66*$A$30+$A$29","v":448.91406890985445},0,0]
[]
[null,{"$f":"B65+1","v":-2},{"$f":"B68*$A$30+$A$29","v":640.94271260656956},{"$f":"$A$65","v":2.0775144411867598E-3},1]
[null,{"$f":"B66+1","v":-2},{"$f":"B69*$A$30+$A$29","v":640.94271260656956},0,0]
[]
[null,{"$f":"B68+1","v":-1},{"$f":"B71*$A$30+$A$29","v":832.97135630328478},{"$f":"$A$65","v":2.0775144411867598E-3},1]
[null,{"$f":"B69+1","v":-1},{"$f":"B72*$A$30+$A$29","v":832.97135630328478},0,0]
[]
[null,{"$f":"B71+1","v":0},{"$f":"B74*$A$30+$A$29","v":1025},{"$f":"$A$65","v":2.0775144411867598E-3},1]
[null,{"$f":"B72+1","v":0},{"$f":"B75*$A$30+$A$29","v":1025},0,0]
[]
[null,{"$f":"B74+1","v":1},{"$f":"B77*$A$30+$A$29","v":1217.0286436967151},{"$f":"$A$65","v":2.0775144411867598E-3},1]
[null,{"$f":"B75+1","v":1},{"$f":"B78*$A$30+$A$29","v":1217.0286436967151},0,0]
[]
[null,{"$f":"B77+1","v":2},{"$f":"B80*$A$30+$A$29","v":1409.0572873934304},{"$f":"$A$65","v":2.0775144411867598E-3},1]
[null,{"$f":"B78+1","v":2},{"$f":"B81*$A$30+$A$29","v":1409.0572873934304},0,0]
[]
[null,{"$f":"B80+1","v":3},{"$f":"B83*$A$30+$A$29","v":1601.0859310901456},{"$f":"$A$65","v":2.0775144411867598E-3},1]
[null,{"$f":"B81+1","v":3},{"$f":"B84*$A$30+$A$29","v":1601.0859310901456},0,0]

{"sheet":"Norminv","index":2,"n_rows":10042,"n_cols":14,"rows_kept":10042,"cut":false,"hidden":false,"merged":[]}
["Simulating Normally Distributed Random Variables"]
[]
[]
[20,"mean"]
[10,"standard deviation"]
[0.25,"graph increment"]
[null,"# SDs","X","Probability","Cum Prob"]
[1,-3.5,{"$f":"B8*$A$5+$A$4","v":-15},{"$f":"_xlfn.NORM.DIST(C8,$A$4,$A$5,0)","v":8.726826950457601E-5},{"$f":"_xlfn.NORM.DIST(C8,$A$4,$A$5,1)","v":2.3262907903552504E-4}]
[{"$f":"1+A8","v":2},{"$f":"B8+$A$6","v":-3.25},{"$f":"B9*$A$5+$A$4","v":-12.5},{"$f":"_xlfn.NORM.DIST(C9,$A$4,$A$5,0)","v":2.0290480572997683E-4},{"$f":"_xlfn.NORM.DIST(C9,$A$4,$A$5,1)","v":5.7702504239076603E-4}]
[3,{"$f":"B9+$A$6","v":-3},-10,4.4318484119380076E-4,1.3498980316300933E-3]
[4,-2.75,-7.5,9.0935625015910518E-4,2.9797632350545551E-3]
[5,-2.5,-5,1.752830049356854E-3,6.2096653257761331E-3]
[6,-2.25,-2.5,3.1739651835667416E-3,1.2224472655044696E-2]
[7,-2,0,5.3990966513188061E-3,2.2750131948179191E-2]
[8,-1.75,2.5,8.6277318826511514E-3,4.00591568638171E-2]
[9,-1.5,5,1.2951759566589173E-2,6.6807201268858057E-2]
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[11,-1,10,2.4197072451914336E-2,0.15865525393145699]
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[]
[]
["Data for Vertical chart lines marking standard deviations from mean.",null,null,null,null,null,"Simulated value with mean and standard deviation from above:"]
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[null,-3,{"$f":"B41*$A$5+$A$4","v":-10},0,0,null,"Build the data table (Green fill), convert the results to values, then sort:"]
[null,null,null,null,null,null,"Data Table",{"$f":"G40","v":17.928861964228854},{"$f":"getformula(H42)","v":"<--  =G40"}]
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[]
[0.15,"mean",null,null,null,null,"Vertical Green Lines"]
[0.2,"standard deviation",null,null,null,null,"X","Y"]
[0.25,"graph increment",null,null,null,null,0.25,{"$f":"_xlfn.NORM.DIST(G4,$A$2,$A$3,0)","v":1.7603266338214976}]
[null,"# SDs","X","Probability","Cum Prob",null,{"$f":"G4","v":0.25},0]
[1,-3.5,{"$f":"B6*$A$3+$A$2","v":-0.55000000000000004},{"$f":"_xlfn.NORM.DIST(C6,$A$2,$A$3,0)","v":4.3634134752288008E-3},{"$f":"_xlfn.NORM.DIST(C6,$A$2,$A$3,1)","v":2.3262907903552504E-4}]
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[]
[]
["Data for Vertical chart lines marking standard deviations from mean."]
[{"$f":"MAX(D6:D34)","v":1.9947114020071635},-3,{"$f":"B38*$A$3+$A$2","v":-0.45000000000000007},{"$f":"_xlfn.NORM.DIST(C38,$A$2,$A$3,0)","v":2.2159242059689999E-2},1]
[null,-3,{"$f":"B39*$A$3+$A$2","v":-0.45000000000000007},0,0]
[]
[null,{"$f":"B38+1","v":-2},{"$f":"B41*$A$3+$A$2","v":-0.25},{"$f":"_xlfn.NORM.DIST(C41,$A$2,$A$3,0)","v":0.26995483256594027},1]
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[]
[null,{"$f":"B41+1","v":-1},{"$f":"B44*$A$3+$A$2","v":-5.0000000000000017E-2},{"$f":"_xlfn.NORM.DIST(C44,$A$2,$A$3,0)","v":1.2098536225957168},1]
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[]
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[]
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[]
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[]
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[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
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["In the examples below note that the stock's rate of return is normally"]
["distributed, NOT the price!"]
[]
["EXAMPLE 1: NORM.DIST"]
["XYZ stock's continuously compounded annual rate of return is normally"]
["distributed as follows:"]
[null,"Mean",0.15]
[null,"Variance",0.04]
[]
["Calculate the probability that the continuously compounded annual rate of"]
["return on XYZ stock is between zero and 20 percent."]
[null,"Rate 1",0]
[null,"Rate 2",0.2]
[null,"Mean Return",0.15]
[null,"Return Standard Deviation",{"$f":"C43^0.5","v":0.2},{"$f":"\"<-- \"&_xlfn.FORMULATEXT(C50)","v":"<-- =C43^0.5"}]
[]
[null,"P(x<Rate1)",{"$f":"NORMDIST(C47,C49,C50,1)","v":0.22662735237686815},{"$f":"\"<-- \"&_xlfn.FORMULATEXT(C52)","v":"<-- =NORMDIST(C47,C49,C50,1)"}]
[null,"P(x>Rate2)",{"$f":"1-NORMDIST(C48,C49,C50,1)","v":0.4012936743170763},"<-- =1-NORMDIST(C48,C49,C50,1)"]
[null,"P(x<Rate1 and x>Rate2)",{"$f":"C52+C53","v":0.62792102669394445},"<-- =C52+C53"]
[null,"P(Rate1<x<Rate2)",{"$f":"1-C54","v":0.37207897330605555},{"$f":"\"<-- \"&_xlfn.FORMULATEXT(C55)","v":"<-- =1-C54"}]
[]
["EXAMPLE 2: NORM.DIST"]
["Assume that XYZ stock (above) is currently priced at $50 per share."]
["Calculate the probability that the price one year from today will be greater"]
["than $75."]
[null,"ROR Needed",{"$f":"LN(75/50)","v":0.40546510810816438},{"$f":"\"<-- \"&_xlfn.FORMULATEXT(C61)","v":"<-- =LN(75/50)"}]
[null,"Mean Return",{"$f":"C42","v":0.15},{"$f":"\"<-- \"&_xlfn.FORMULATEXT(C62)","v":"<-- =C42"}]
[null,"Return Standard Deviation",{"$f":"C50","v":0.2},{"$f":"\"<-- \"&_xlfn.FORMULATEXT(C63)","v":"<-- =C50"}]
[null,{"$f":"\"P(Return>\"&FIXED(C61*100,2)&\"%)\"","v":"P(Return>40.55%)"},{"$f":"1-NORMDIST(C61,C62,C63,1)","v":0.10074367012050367},{"$f":"\"<-- \"&_xlfn.FORMULATEXT(C64)","v":"<-- =1-NORMDIST(C61,C62,C63,1)"}]
[]
["EXAMPLE 3: NORM.INV"]
["What continuously compounded annual rate of return on XYZ stock (R) has"]
["only a ten percent chance of being higher than that rate (R) ?"]
[null,"The answer to this question is not a probability - it is a rate of"]
[null,"return, specifically the 90%ile rate."]
[]
[null,"Rate of Return",{"$f":"_xlfn.NORM.INV(1-10%,C62,C63)","v":0.40631031310892007},{"$f":"\"<-- \"&_xlfn.FORMULATEXT(C72)","v":"<-- =NORM.INV(1-10%,C62,C63)"}]
[]
["90% of the time ROR will be lower than this & 10% of the time higher!"]

{"sheet":"StockSim","index":5,"n_rows":257,"n_cols":10,"rows_kept":257,"cut":false,"hidden":false,"merged":[]}
["CONCEPTUALIZING THE LOGNORMAL DISTRIBUTION"]
[null,0.1,"Mean (Annual Return)"]
[null,0.4,"Sigma (Return Annual StDev)"]
[null,{"$f":"1/250","v":4.0000000000000001E-3},"Dt (Time Increment in Years)"]
[null,50,"Initial stock price"]
["Time","Normal\ndeviates","Continuous Return","Stock\nprice"]
[0,null,null,{"$f":"B5","v":50},{"$f":"getformula(D7)","v":"<--  =B5"}]
[1,{"$f":"_xlfn.NORM.INV(RAND(),0,1)","v":0.543609380465643},{"$f":"LN(D8/D7)","v":1.4152350397635741E-2},{"$f":"D7*EXP(Mean*deltat+Sigma*SQRT(deltat)*B8)","v":50.712648450574505},{"$f":"getformula(D8)","v":"<--  =D7*EXP(Mean*deltat+Sigma*SQRT(deltat)*B8)"}]
[2,{"$f":"_xlfn.NORM.INV(RAND(),0,1)","v":-0.61108448833017137},{"$f":"LN(D9/D8)","v":-1.5059350607375371E-2},49.95467054953108]
[3,-1.646482566668575,-4.1253080307461873E-2,47.935814824365764]
[4,-1.2056726470874433,-3.0101373418885545E-2,46.514381832388196]
[5,-0.80311678475230019,-1.9917426135427664E-2,45.597100335132374]
[6,-0.62351345690570603,-1.537378140469811E-2,44.901461483032158]
[7,-1.0384070557814011,-2.586985147726998E-2,43.754763744940774]
[8,-0.9649435161126293,-2.4011354594618357E-2,42.716665544844759]
[9,0.58322609599510267,1.5154582833540172E-2,43.368948848250376]
[10,5.9864622811534846E-2,1.9144684748105829E-3,43.452056862058363]
[11,-1.8845334530976512,-4.7275344308565455E-2,41.445646457368795]
[12,-1.0530560054463525,-2.6240443847433143E-2,40.372239231284112]
[13,1.0794182795585021,2.7707362491401998E-2,41.506488463094477]
[14,0.57547913421699082,1.4958598480219423E-2,42.132034338846282]
[15,0.9120023292638697,2.3472036734821199E-2,43.132656375650761]
[16,-0.44876113791403643,-1.0952858569418534E-2,42.662808277633815]
[17,-0.42993913593680483,-1.0476695398440409E-2,42.218176234642513]
[18,-0.64956162007908114,-1.6032753600630893E-2,41.546699809121527]
[19,1.7800193903058992,4.5431324421046998E-2,43.477754461140911]
[20,1.178855080637826,3.0222936688615892E-2,44.81183829993315,null,"Research has found that most stocks and portfolios of stocks"]
[21,1.0419526155810652,2.6759547833648211E-2,46.027171188283077,null,"have continuously compounded returns that are approximately"]
[22,0.53431029194936575,1.3917099998636122E-2,46.672214084345065,null,"normally distributed and independent."]
[23,0.36202697976808945,9.5586386439909469E-3,47.120475886741602]
[24,0.66064004945289656,1.7113018158379328E-2,47.93378871634328,null,"StDev","Bin","Frequency","X:Return","Y: Probability"]
[25,-0.47236184864713371,-1.1549914571941327E-2,47.383342474234375,null,-3,{"$f":"($F32+0.5)*Sigma*deltat^0.5+Mean*deltat","v":-6.2845553203367585E-2},{"$f":"FREQUENCY(C8:C257,G32:G38)","v":2},{"$f":"($F32)*Sigma*deltat^0.5+Mean*deltat","v":-7.5494663844041118E-2},{"$f":"H32/$H$39","v":8.0000000000000002E-3}]
[26,0.60930018295692612,1.5814210855209468E-2,48.138629032904561,null,{"$f":"F32+1","v":-2},-3.754733192202056E-2,11,-5.0196442562694073E-2,4.3999999999999997E-2]
[27,-1.2536656006900349,-3.1315509779069377E-2,46.654502694543005,null,{"$f":"F33+1","v":-1},-1.2249110640673518E-2,80,-2.4898221281347034E-2,0.32]
[28,0.94913529534542695,2.4411434727585345E-2,47.807420983420975,null,0,1.3049110640673517E-2,75,4.0000000000000002E-4,0.3]
[29,1.7714980666962843,4.5215750090761161E-2,50.018684630738072,null,1,3.8347331922020556E-2,65,2.5698221281347036E-2,0.26]
[30,0.78522167986764146,2.0264711812202567E-2,51.042638887913419,null,2,6.364555320336758E-2,16,5.0996442562694068E-2,6.4000000000000001E-2]
[31,1.4624542326255603,3.7397490790803976E-2,52.987648055837383,null,3,{"$f":"(2*$F38+0.5)*Sigma*deltat^0.5+Mean*deltat","v":0.16483843832875572},1,7.6294663844041113E-2,4.0000000000000001E-3]
[32,1.6735129534017634,4.2736901012358441E-2,55.30126214423624,null,null,null,{"$f":"SUM(H32:H38)","v":250}]
[33,-1.4930385846847749,-3.7371220496944628E-2,53.272726983828768]
[34,0.55403346857650293,1.4416061285320652E-2,54.046272221994123]
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{"sheet":"StockSim (2)","index":6,"n_rows":257,"n_cols":10,"rows_kept":257,"cut":false,"hidden":false,"merged":[]}
["CONCEPTUALIZING THE LOGNORMAL DISTRIBUTION"]
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[20,null,3.5899602714341429E-2,48.40062746334543,null,"Research has found that most stocks and portfolios of stocks"]
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[238,null,-4.149093009530213E-2,42.697504727803455]
[239,null,8.2410747649643758E-3,43.050831954898342]
[240,null,-2.7131443665764639E-2,41.898503585408882]
[241,null,6.5169430593374584E-3,42.17244540964392]
[242,null,6.079074361315346E-3,42.429595667138059]
[243,null,-8.8180458635344159E-3,42.05709432726502]
[244,null,-3.1327720433475738E-2,40.75996556219205]
[245,null,-1.3201533049669234E-2,40.225407784364265]
[246,null,-4.3670593610944837E-2,38.506545383368511]
[247,null,-2.6350593559425432E-2,37.505126985404651]
[248,null,2.3038346593494706E-2,38.379213189503595]
[249,null,2.693022374043174E-2,39.426816774509206]
[250,null,-5.1081979265195981E-3,39.225930311541362]

{"sheet":"Quiz","index":7,"n_rows":98,"n_cols":18,"rows_kept":98,"cut":false,"hidden":false,"merged":[]}
[null,null,null,null,"Sample Quiz A: No computer or calculator"]
[null,null,null,null,"Ruler and colored pencils recommended"]
[null,"Name__________________________",null,null,null,null,null,null,null,"2-digit Class # ________"]
[]
[null,"Using the graph below illustrate how to estimate the probability that the return on your investment in XYZ ",null,null,null,null,null,null,null,null,null,null,null,null,null,"Rate 1",0]
[null,"stock is between",null,{"$f":"Q5","v":0},"and",{"$f":"Q6","v":0.15},". Assume that the expected return on XYZ is",null,null,null,null,{"$f":"Q7","v":0.1},null,null,null,"Rate 2",0.15]
[null,"and the standard deviation of XYZ's return is",null,null,null,null,{"$f":"Q8","v":0.2},"and returns are normally distributed.",null,null,null,null,null,null,null,"Mean",0.1]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Std",0.2]
[null,"Put your answer to the above question in the space to the right: _________________"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"St Devs"]
[null,"Show how you arrived at this answer by completing the graph below with the following:",null,null,null,null,null,null,null,null,null,null,null,null,null,"P(x<Rate1)",{"$f":"NORMDIST(Q5,Q7,Q8,1)","v":0.30853753872598688},{"$f":"(Q5-Q7)/Q8","v":-0.5}]
[null,null,"Below the horizontal axis label the standard deviation scale: -3, -2, -1, 0, 1, 2, 3",null,null,null,null,null,null,null,null,null,null,null,null,"P(x>Rate2)",{"$f":"1-NORMDIST(Q6,Q7,Q8,1)","v":0.4012936743170763},{"$f":"(Q6-Q7)/Q8","v":0.24999999999999994}]
[null,null,"Below the standard deviation scale add the rates of return for the stock as shown in class",null,null,null,null,null,null,null,null,null,null,null,null,"P(x<Rate1 and x>Rate2)",{"$f":"Q11+Q12","v":0.70983121304306318}]
[null,null,"Shade or crosshatch the area to be estimated",null,null,null,null,null,null,null,null,null,null,null,null,"P(Rate1<x<Rate2)",{"$f":"1-Q13","v":0.29016878695693682},"<-- Answer"]
[null,null,"Label key areas of the graph with percentages used to arrive at your answer above"]
[null,null,"Show any calculations in the space provided below the graph"]
[null,"Your answer will be graded on completeness, neatness and a reasonable level of numeric accuracy."]
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[null,"Perform any calculations below. Be sure to enter your answer above."]
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[null,null,null,null,"Sample Quiz B: No computer or calculator"]
[null,null,null,null,"Ruler and colored pencils recommended"]
[null,"Name__________________________",null,null,null,null,null,null,null,"2-digit Class # ________"]
[]
[null,"Using the graph below illustrate how to estimate the probability that the return on your investment in XYZ ",null,null,null,null,null,null,null,null,null,null,null,null,null,"Rate 1",0]
[null,"stock is between",null,{"$f":"Q57","v":0},"and",{"$f":"Q58","v":0.2},". Assume that the expected return on XYZ is",null,null,null,null,{"$f":"Q59","v":0.15},null,null,null,"Rate 2",0.2]
[null,"and the standard deviation of XYZ's return is",null,null,null,null,{"$f":"Q60","v":0.1},"and returns are normally distributed.",null,null,null,null,null,null,null,"Mean",0.15]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Std",0.1]
[null,"Put your answer to the above question in the space to the right: _________________"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"St Devs"]
[null,"Show how you arrived at this answer by completing the graph below with the following:",null,null,null,null,null,null,null,null,null,null,null,null,null,"P(x<Rate1)",{"$f":"NORMDIST(Q57,Q59,Q60,1)","v":6.6807201268858085E-2},{"$f":"(Q57-Q59)/Q60","v":-1.4999999999999998}]
[null,null,"Below the horizontal axis label the standard deviation scale: -3, -2, -1, 0, 1, 2, 3",null,null,null,null,null,null,null,null,null,null,null,null,"P(x>Rate2)",{"$f":"1-NORMDIST(Q58,Q59,Q60,1)","v":0.30853753872598688},{"$f":"(Q58-Q59)/Q60","v":0.50000000000000011}]
[null,null,"Below the standard deviation scale add the rates of return for the stock as shown in class",null,null,null,null,null,null,null,null,null,null,null,null,"P(x<Rate1 and x>Rate2)",{"$f":"Q63+Q64","v":0.37534473999484497}]
[null,null,"Shade or crosshatch the area to be estimated",null,null,null,null,null,null,null,null,null,null,null,null,"P(Rate1<x<Rate2)",{"$f":"1-Q65","v":0.62465526000515503},"<-- Answer"]
[null,null,"Label key areas of the graph with percentages used to arrive at your answer above"]
[null,null,"Show any calculations in the space provided below the graph"]
[null,"Your answer will be graded on completeness, neatness and a reasonable level of numeric accuracy."]
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[null,"Perform any calculations below. Be sure to enter your answer above."]