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[null,-0.9,0.1840601253467595,0.18141125489179724,0.17878637961437172,0.1761855422452579,0.17360878033862448,0.17105612630848177,0.16852760746683779,0.16602324606352964,0.16354305932769236,0.16108705951083091,null,2.2000000000000002,0.98609655248650141,0.98644741885358,0.98679061619274377,0.98712627856139801,0.98745453856405341,0.98777552734495533,0.98808937458145296,0.98839620847809651,0.9886961557614472,0.98898934167558861]
[null,-0.8,0.21185539858339661,0.2089700878716016,0.20610805358581305,0.20326939182806841,0.20045419326044966,0.19766254312269235,0.19489452125180831,0.19215020210369613,0.18942965477671211,0.18673294303717258,null,2.2999999999999998,0.98927588997832416,0.98955592293804895,0.98982956133128031,0.99009692444083575,0.99035813005464168,0.99061329446516144,0.99086253246942735,0.99110595736966323,0.99134368097448344,0.99157581360065428]
[null,-0.7,0.24196365222307298,0.23885206808998671,0.23576249777925118,0.23269509230089741,0.22964999716479059,0.22662735237686821,0.22362729243759941,0.22064994634264959,0.21769543758573318,0.21476388416363718,null,2.4,0.99180246407540384,0.99202373973926627,0.99223974644944635,0.99245058858369084,0.99265636904465171,0.99285718926472855,0.99305314921137566,0.99324434739285938,0.99343088086445319,0.99361284523505677]
[null,-0.6,0.27425311775007355,0.27093090378300566,0.267628893468983,0.26434729211567748,0.26108629969286151,0.25784611080586467,0.25462691467133614,0.25142889509531008,0.24825223045357048,0.24509709367430943,null,2.5,0.99379033467422384,0.9939634419195873,0.99413225828466745,0.99429687366704933,0.99445737655691735,0.99461385404593328,0.99476639183644422,0.994915074251009,0.99505998424222941,0.99520120340287377]
[null,-0.5,0.30853753872598688,0.30502573089751939,0.30153178754696619,0.29805596539487639,0.29459851621569799,0.29115968678834636,0.28773971884902705,0.28433884904632412,0.2809573088985643,0.27759532475346493,null,2.6,0.99533881197628127,0.99547288886703267,0.99560351165187866,0.9957307565909107,0.99585469863896392,0.99597541145724167,0.99609296742514719,0.99620743765231456,0.99631889199082502,0.99642739904760025]
[null,-0.4,0.34457825838967576,0.34090297377232259,0.33724272684824946,0.33359782059545762,0.32996855366059363,0.32635522028791997,0.32275811025034773,0.3191775087825558,0.31561369651622251,0.31206694941739055,null,2.7,0.99653302619695938,0.9966358395933308,0.99673590418410873,0.99683328372264224,0.99692804078134956,0.99702023676494544,0.99710993192377384,0.99719718536723501,0.99728205507729872,0.99736459792209509]
[null,-0.3,0.38208857781104733,0.37828047817798072,0.37448416527667994,0.37069998105934648,0.36692826396397193,0.3631693488243809,0.35942356678200876,0.35569124519945322,0.35197270757583721,0.34826827346401756,null,2.8,0.99744486966957202,0.99752292500121409,0.9975988175258107,0.9976725997932685,0.99774432330845764,0.99781403854508677,0.99788179495959539,0.99794764100506028,0.99801162414510569,0.99807379086781212]
[null,-0.2,0.42074029056089696,0.41683383651755768,0.41293557735178538,0.40904588485799409,0.40516512830220414,0.4012936743170763,0.39743188679823949,0.39358012680196047,0.38973875244420275,0.38590811880112263,null,2.9,0.99813418669961596,0.99819285621919351,0.99824984307132392,0.99830518998072271,0.99835893876584303,0.99841113035263518,0.99846180478826196,0.99851100125476255,0.99855875808266004,0.9986051127645077]
[null,-0.1,0.46017216272297101,0.45620468745768322,0.45224157397941611,0.44828321334543886,0.44432999519409355,0.44038230762975744,0.43644053710856717,0.43250506832496155,0.42857628409909926,0.42465456526520451,null,3,0.9986501019683699,0.99869376155123057,0.99873612657232769,0.99877723130640772,0.9988171092568956,0.99885579316897732,0.99889331504259071,0.99892970614532106,0.99896499702519714,0.99899921752338594]
[null,0,0.5,0.4960106436853684,0.492021686283098,0.48803352658588733,0.48404656314716926,0.48006119416162751,0.47607781734589316,0.47209682981947887,0.46811862798601261,0.46414360741482791,null,3.1,0.99903239678678168,0.99906456328048587,0.99909574480017771,0.99912596848436841,0.99915526082654138,0.99918364768717138,0.99921115430562446,0.99923780531193274,0.9992636247384461,0.99928863603135465]
[]
[null,"Example : Using the Z-score above"]
[]
[null,"Case 1:","P (Z)   <",null,{"$f":"IF(F4=\"\",\"\",F4)","v":""},{"$f":"IF(F4=\"\",\"\",\"=\")","v":""},{"$f":" J4","v":""},null,null,"Area to the left, directly from the table",null,null,null,null,null,{"$f":"IF(F4=\"\",\"\",IF($E$52>=-3.19,\"x\",\"\"))","v":""},{"$f":"IF(F4=\"\",\"\",IF($E$52>=-2.01,\"x\",\"\"))","v":""},{"$f":"IF(F4=\"\",\"\",IF($E$52>=-1.01,\"x\",\"\"))","v":""},{"$f":"IF(F4=\"\",\"\",IF($E$52>=-0.5,\"x\",\"\"))","v":""},{"$f":"IF(F4=\"\",\"\",IF($E$52>0,\"x\",\"\"))","v":""},{"$f":"IF(F4=\"\",\"\",IF($E$52>0.5,\"x\",\"\"))","v":""},{"$f":"IF(F4=\"\",\"\",IF($E$52>1,\"x\",\"\"))","v":""},{"$f":"IF(F4=\"\",\"\",IF($E$52>2,\"x\",\"\"))","v":""},{"$f":"IF(F4=\"\",\"\",IF($E$52>3.19,\"x\",\"\"))","v":""},null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"IF(G52=\"\",\"\",ROUND(G52,4))","v":""}]
[null,null,null,null,null,{"$f":"IF(F4=\"\",\"\",\"=\")","v":""},{"$f":"G52","v":""},null,null,null,null,null,null,null,null,"P (Z)   <",{"$f":"IF(F4=\"\",\"\",F4&\"  =  \"&TEXT(G52,\"0.0000\")&\" = \")","v":""},null,{"$f":"G53","v":""}]
[]
[null,"Case 2:","P (Z)   > ",null,{"$f":"IF(F4=\"\",\"\",F4)","v":""},{"$f":"IF(F4=\"\",\"\",\"=\")","v":""},{"$f":"IF(F4=\"\",\"\",\" 1  -  \"&TEXT(J4,\" 0.0000\")&\"   =  \"&TEXT(AS55,\"0.0000\"))","v":""},null,null,"Area to the right, 1 - (left area )",null,null,null,null,null,{"$f":"IF($E$55<=-3.19,\"x\",\"\")","v":""},{"$f":"IF($E$55<=-2.01,\"x\",\"\")","v":""},{"$f":"IF($E$55<=-1.01,\"x\",\"\")","v":""},{"$f":"IF($E$55<=-0.5,\"x\",\"\")","v":""},{"$f":"IF($E$55<=0,\"x\",\"\")","v":""},{"$f":"IF($E$55<=0.5,\"x\",\"\")","v":""},{"$f":"IF($E$55<=1.01,\"x\",\"\")","v":""},{"$f":"IF($E$55<=2,\"x\",\"\")","v":""},{"$f":"IF(AND($E$55<=3.19,F4<>0),\"x\",\"\")","v":""},{"$f":"IF($E$52>-2,\"x\",\"\")","v":"x"},{"$f":"IF($E$52>-1,\"x\",\"\")","v":"x"},{"$f":"IF($E$52>-0.5,\"x\",\"\")","v":"x"},{"$f":"IF($E$52>=0,\"x\",\"\")","v":"x"},{"$f":"IF($E$52>0.5,\"x\",\"\")","v":"x"},{"$f":"IF($E$52>1,\"x\",\"\")","v":"x"},{"$f":"IF($E$52>2,\"x\",\"\")","v":"x"},{"$f":"IF($E$52>2,\"x\",\"\")","v":"x"},null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"IF(G52=\"\",\"\",1-G52)","v":""}]
[null,null,null,null,null,{"$f":"IF(F4=\"\",\"\",\"=\")","v":""},{"$f":"IF(F4=\"\",\"\",AS55)","v":""},null,null,null,"or,  1- (Table Value)",null,null,null,null,null,null,"P (Z)   >",{"$f":"IF(F4=\"\",\"\",F4&\"  =  \")","v":""},{"$f":"IF(F4=\"\",\"\",G55&\" = \")","v":""},null,null,{"$f":"IF(F4=\"\",\"\",G56)","v":""},null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"IF(V59=\"\",\"\",V59/100)","v":""}]
[]
[]
[null,"Case 3: ","Between two Z-scores such as:",null,null,null,"Z = ",null,"      and ","Z =",null,null,null,"Case 4","If Probability is given, \nfind nearest Z-score",null,null," Enter Probabilty  (0 - 100%) = ",null,null,null,null,"%",null,{"$f":"IF($E$52>-2,\"x\",\"\")","v":"x"},{"$f":"IF($E$52>-1,\"x\",\"\")","v":"x"},{"$f":"IF($E$52>-0.5,\"x\",\"\")","v":"x"},{"$f":"IF($E$52>=0,\"x\",\"\")","v":"x"},{"$f":"IF($E$52>0.5,\"x\",\"\")","v":"x"},{"$f":"IF($E$52>1,\"x\",\"\")","v":"x"},{"$f":"IF($E$52>2,\"x\",\"\")","v":"x"},{"$f":"IF($E$52>2,\"x\",\"\")","v":"x"},null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"IF(K60=\"\",\"\",K60-H60)","v":""},{"$f":"V59*100","v":0},{"$f":"IF(V59=\"\",\"\",IF(OR(AU56>0.97,AU56<0.05,AU56=19),NORMSINV(AU56+0.0001),IF(AY59<>0,NORMSINV(AU56+0.002),NORMSINV(AU56+0.0007))))","v":""},{"$f":"IF(V60<0,LEFT(V60,4),LEFT(V60,3))","v":""},{"$f":"IF(AND(V60>=0,AW60=3),0,IF(AND(V60<0,AW60=5),0,IF(AND(V60>=0,AW60=1),0,IF(AND(V60<0,AW60=3),0,RIGHT(V60,1)))))","v":""},{"$f":"RIGHT(V59,1)","v":""},{"$f":"IFERROR(VLOOKUP(V59,AZ16:AZ32,1,FALSE),0)","v":0}]
[null,null,null," (Enter any z-score)",null,null,"P =",{"$f":"IF(OR(H59=\"\",H59<-3.19,H59>=3.19),\"\",NORMSDIST(H59))","v":""},null,"P =",{"$f":"IF(OR(K59=\"\",K59<-3.19,K59>=3.19),\"\",NORMSDIST(K59))","v":""},null,null,null,null,null,null,{"$f":"IF(OR(AU56=\"\",AU56>100%,AU56<0),\"\",\"Covering at least \"&AT59/100&\" % ,   Z = \")","v":""},null,null,null,{"$f":"IF(OR(AU56=\"\",AU56>=100%,AU56<=0,AU63<>AU64),\"\",ROUND(AU59,2))","v":""},null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"IF(V59=\"\",\"\",NORMSDIST(V60))","v":""},null,{"$f":"IF(V60<0,LEN(V60)+1,LEN(V60))","v":0}]
[]
[null,null,{"$f":"IF(OR(H60=\"\",K60=\"\",K59<=H59,H59<=-3.19,K59>=3.19),\"\",\" Then  Subtract,  P =  \"&TEXT(K60,\"0.0000\")&\"  -  \"&TEXT(H60,\"0.0000\")&\"  =  \"&TEXT(AS59,\"0.0000\"))","v":""},null,null,null,null,null,null,{"$f":"IF(OR(H59=\"\",K59=\"\",H59>=K59),\"\",\"Or\")","v":""},{"$f":"IF(OR(H59=\"\",K59=\"\",H59=\"\"),\"\",IF(K59<H59,\"Change Z-cores\",AS59))","v":""},null,null,null,{"$f":"IF(OR(AU56=\"\",AU56>100%,AU56<0,AU63<>AU64),\"\",\"Row =\")","v":""},{"$f":"IF(OR(AU56=\"\",AU56>=100%,AU56<=0,AU63<>AU64),\"\",AV59*1)","v":""},{"$f":"IF(OR(AU56=\"\",AU56>100%,AU56<0,AU63<>AU64),\"\",\"Column =\")","v":""},{"$f":"IF(OR(AU56=\"\",AU56>=100%,AU56<=0,AU63<>AU64),\"\",(AW59*1)/100)","v":""},null,{"$f":"IF(OR(V59=\"\",V59>100,V59<0,AU63<>AU64),\"\",\"(See table score highlighted in yellow)\")","v":""}]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"V59","v":0}]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"ROUND(AU63,0)","v":0}]

{"sheet":"Sec 5.3","index":1,"n_rows":36,"n_cols":22,"rows_kept":36,"cut":false,"hidden":false,"merged":[[28,14,28,16],[30,1,30,2],[23,13,23,14],[16,13,16,14],[26,2,26,3],[26,4,26,6],[26,14,26,15],[26,16,26,18],[19,2,19,3],[19,4,19,6],[19,14,19,15],[19,16,19,18],[12,16,12,18],[1,1,1,9],[2,4,2,10],[4,1,4,2],[4,13,4,14],[12,2,12,3],[12,4,12,6],[12,14,12,15]]}
[]
[null,"First, read the example below, then use the template to solve a problem.",null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Fill Green Cells Only"]
[null,"Example:",null,null,"Let X to be a normal variable with mean 400 and standard deviation 40. Find the following cases:",null,null,null,null,null,null,null,null,"Section 5.3: Random Variable Template"]
[]
[null,"Given:",null,null,null,null,null,null,null,null,null,null,null,"Given:",null,null,null,null,"Fill"]
[null,null,null,"Expected Value, Mean =",null,null,400,null,null,null,null,null,null,null,null,"Expected Value, Mean ="]
[null,null,null,"Standard Deviation =",null,null,40,null,null,null,null,null,null,null,null,"Standard Deviation ="]
[]
[]
[null,null,null,"To find Z-score:"," If x  =",350,{"$f":"  \" Then  Z =  (\"&F10&\" - \"&G6&\") / \"&G7","v":" Then  Z =  (350 - 400) / 40"},null,null,null,null,null,null,null,null,"To find Z-score:"," If x  =",null,{"$f":"IF(OR(S6=\"\",S7=\"\",R10=\"\"),\"\", \" Then  Z =  (\"&R10&\" - \"&S6&\") / \"&S7)","v":""}]
[null,null,null,null,null,null,"Z =",{"$f":"(F10-G6)/G7","v":-1.25},null,null,null,null,null,null,null,null,null,null,{"$f":"IF(T11=\"\",\"\",\" Z = \")","v":""},{"$f":"IF(OR(S6=\"\",S7=\"\",R10=\"\"),\"\",(R10-S6)/S7)","v":""}]
[]
[null,null,"Case 1: ",null,"Pr ( x < 350)",null,null,null,null,null,null,null,null,null,"Case 1:",null,"Pr( x < a)  "]
[]
[]
[null,null,null,null,null,null,null,null,null,"Answer:",null,null,null,null,null,null,null,null,null,null,null,"Answer:"]
[null,null,null,"Pr( x < ",350," or P ( Z <",-1.25,"P =",null,0.1056,null,null,null,"Pr( x < ",null,null,"or","P ( Z <",{"$f":"IF(OR(S6=\"\",S7=\"\",P17=\"\"),\"\",(P17-S6)/S7)","v":""},"P =",null,{"$f":"IF(OR(S6=\"\",S7=\"\",P17=\"\"),\"\",NORMSDIST(S17))","v":""}]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"V17","v":""}]
[]
[null,null,"Case 2:",null,"Pr (x > 420)",null,null,null,null,null,null,null,null,null,"Case 2:",null,"Pr( x > b) "]
[]
[]
[null,null,null,null,null,null,null,null,null,"Answer:",null,null,null,null,null,null,null,null,null,null,null,"Answer:"]
[null,null,null,"Pr( x > ",420," or P ( Z >",0.5,"P =",null,0.3085,null,null,null,"Pr( x > ",null,null,"or","P( Z >",{"$f":"IF(OR(S6=\"\",S7=\"\",P24=\"\"),\"\",(P24-S6)/S7)","v":""},"P =",null,{"$f":"IF(OR(S6=\"\",S7=\"\",P24=\"\"),\"\",1-NORMSDIST(S24))","v":""}]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"V24","v":""}]
[]
[null,null,"Case 3:",null,"Pr (360 < x < 410)",null,null,null,null,null,null,null,null,null,"Case 3:",null,"Pr( a < x < b) "]
[]
[]
[]
[null,360,null,"< x <",410,-1," < Z <",0.25,null,null,null,null,null,null,null,"< x <",null,{"$f":"IF(OR(S6=\"\",S7=\"\",O31=\"\"),\"\",(O31-S6)/S7)","v":""}," < Z <",{"$f":"IF(OR(S6=\"\",S7=\"\",Q31=\"\"),\"\",(Q31-S6)/S7)","v":""}]
[null,null,null,null,null,0.15865525393145707," < P <",0.5987063256829237,null,"Answer:",null,null,null,null,null,null,null,{"$f":"IF(OR(S6=\"\",S7=\"\",O31=\"\",Q31=\"\"),\"\",NORMSDIST(R31))","v":""}," < P <",{"$f":"IF(OR(S6=\"\",S7=\"\",O31=\"\",Q31=\"\"),\"\",NORMSDIST(T31))","v":""},null,"Answer:"]
[null,null,null,null,null,null,null,"P =",null,0.44009999999999999,null,null,null,null,null,{"$f":"IF(V33<0,\"Error, negative answer\",\"\")","v":""},null,null,null,"P =",null,{"$f":"IF(OR(R32=\"\",T32=\"\"),\"\",(T32-R32))","v":""}]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"V33","v":""}]
[]
[null,null,null,"The above is just an example already filled and solved",null,null,null,null,null,null,null,null,null,null,null,"Make sure to Allow Macro when you start the file"]

{"sheet":"Z <  0","index":2,"n_rows":35,"n_cols":15,"rows_kept":35,"cut":false,"hidden":false,"merged":[]}
[]
[null,null,null,null,"Area Under The Standard Normal Curve (Z < 0)"]
[null,"Z",0,0.01,0.02,0.03,0.04,0.05,0.06,7.0000000000000007E-2,0.08,0.09]
[null,-3.1,{"$f":"NORMSDIST(B4-$C$3)","v":9.676032132183561E-4},{"$f":"NORMSDIST(B4-+$D$3)","v":9.3543671951410031E-4},{"$f":"NORMSDIST(B4-$E$3)","v":9.0425519982233952E-4},{"$f":"NORMSDIST(B4-$F$3)","v":8.7403151563156744E-4},{"$f":"NORMSDIST(B4-$G$3)","v":8.4473917345862643E-4},{"$f":"NORMSDIST(B4-$H$3)","v":8.1635231282856167E-4},{"$f":"NORMSDIST(B4-$I$3)","v":7.8884569437557184E-4},{"$f":"NORMSDIST(B4-$J$3)","v":7.6219468806723459E-4},{"$f":"NORMSDIST(B4-$K$3)","v":7.3637526155392961E-4},{"$f":"NORMSDIST(B4-$L$3)","v":7.1136396864536315E-4},null,"Example:  For Z - Score = -1.67"]
[null,-3,{"$f":"NORMSDIST(B5-$C$3)","v":1.3498980316300933E-3},{"$f":"NORMSDIST(B5-+$D$3)","v":1.3062384487694675E-3},{"$f":"NORMSDIST(B5-$E$3)","v":1.2638734276722969E-3},{"$f":"NORMSDIST(B5-$F$3)","v":1.2227686935922593E-3},{"$f":"NORMSDIST(B5-$G$3)","v":1.1828907431044044E-3},{"$f":"NORMSDIST(B5-$H$3)","v":1.1442068310226975E-3},{"$f":"NORMSDIST(B5-$I$3)","v":1.1066849574092469E-3},{"$f":"NORMSDIST(B5-$J$3)","v":1.0702938546789222E-3},{"$f":"NORMSDIST(B5-$K$3)","v":1.0350029748028415E-3},{"$f":"NORMSDIST(B5-$L$3)","v":1.0007824766140115E-3},null,null,"First two digits for Row of -1.6"]
[null,-2.9,1.8658133003840378E-3,1.807143780806431E-3,1.7501569286760988E-3,1.6948100192772627E-3,1.6410612341569962E-3,1.5888696473648693E-3,1.538195211738057E-3,1.4889987452374655E-3,1.4412419173400134E-3,1.3948872354922507E-3,null,null,"Third digit is for column 0.07"]
[null,-2.8,2.5551303304279312E-3,2.4770749987858636E-3,2.4011824741892529E-3,2.3274002067315554E-3,2.2556766915423207E-3,2.1859614549132396E-3,2.1182050404046204E-3,2.0523589949397532E-3,1.9883758548943252E-3,1.9262091321878626E-3,null,null,"The value is = 0.0475"]
[null,-2.7,3.4669738030406643E-3,3.3641604066691941E-3,3.2640958158913066E-3,3.1667162773577947E-3,3.071959218650487E-3,2.9797632350545551E-3,2.8900680762261443E-3,2.8028146327650242E-3,2.7179449227012539E-3,2.6354020779049505E-3]
[null,-2.6,4.6611880237187476E-3,4.5271111329673241E-3,4.3964883481213092E-3,4.2692434090893508E-3,4.1453013610360367E-3,4.0245885427583044E-3,3.9070325748527717E-3,3.7925623476854869E-3,3.6811080091749787E-3,3.5726009523997363E-3]
[null,-2.5,6.2096653257761331E-3,6.0365580804126653E-3,5.8677417153325615E-3,5.7031263329506993E-3,5.5426234430825993E-3,5.3861459540666869E-3,5.2336081635557816E-3,5.0849257489910355E-3,4.9400157577706438E-3,4.7987965971261785E-3]
[null,-2.4,8.1975359245961311E-3,7.9762602607337287E-3,7.7602535505536425E-3,7.5494114163092126E-3,7.3436309553483459E-3,7.1428107352714204E-3,6.9468507886243092E-3,6.7556526071406503E-3,6.569119135546763E-3,6.3871547649431782E-3]
[null,-2.2999999999999998,1.0724110021675811E-2,1.044407706195109E-2,1.0170438668719676E-2,9.9030755591642573E-3,9.6418699453583289E-3,9.3867055348385835E-3,9.1374675305726672E-3,8.8940426303367806E-3,8.6563190255165429E-3,8.4241863993456938E-3]
[null,-2.2000000000000002,1.3903447513498597E-2,1.3552581146419981E-2,1.3209383807256267E-2,1.287372143860201E-2,1.2545461435946561E-2,1.2224472655044696E-2,1.1910625418547057E-2,1.1603791521903535E-2,1.1303844238552777E-2,1.1010658324411384E-2]
[null,-2.1,1.7864420562816546E-2,1.7429177937657091E-2,1.7003022647632787E-2,1.6585806683605007E-2,1.6177383372166076E-2,1.5777607391090503E-2,1.538633478392545E-2,1.5003422973732208E-2,1.4628730775989252E-2,1.4262118410668875E-2]
[null,-2,2.2750131948179191E-2,2.2215594429431475E-2,2.1691693767646781E-2,2.1178269642672266E-2,2.0675162866070039E-2,2.0182215405704397E-2,1.9699270409376895E-2,1.9226172227517276E-2,1.8762766434937749E-2,1.8308899851658973E-2]
[null,-1.9,2.87165598160018E-2,2.8066606659772512E-2,2.7428949703836809E-2,2.6803418877054948E-2,2.6189844940452685E-2,2.5588059521638607E-2,2.4997895148220432E-2,2.441918528022255E-2,2.3851764341508513E-2,2.329546775021182E-2]
[null,-1.8,3.5930319112925789E-2,3.5147893584038796E-2,3.4379502445889977E-2,3.3624969419628316E-2,3.2884118659163887E-2,3.2156774795613713E-2,3.1442762980752693E-2,3.074190892946595E-2,3.0054038961199774E-2,2.9378980040409414E-2]
[null,-1.7,4.4565462758543041E-2,4.3632936524031884E-2,4.2716220791328911E-2,4.181513761359492E-2,4.0929508978807365E-2,4.00591568638171E-2,3.9203903287482647E-2,3.8363570362871233E-2,3.7537980348516783E-2,3.6726955698726291E-2]
[null,-1.6,5.4799291699557967E-2,5.3698928148119669E-2,5.2616138454252052E-2,5.1550748490089351E-2,5.0502583474103704E-2,4.9471468033648082E-2,4.845722626672281E-2,4.7459681802947302E-2,4.6478657863720019E-2,4.551397732154977E-2]
[null,-1.5,6.6807201268858057E-2,6.5521712088916481E-2,6.4255487818935766E-2,6.3008364463978436E-2,6.1780176711811879E-2,6.057075800205898E-2,5.9379940594793013E-2,5.8207555638553017E-2,5.7053433237754192E-2,5.5917402519469417E-2]
[null,-1.4,8.0756659233771053E-2,7.9269841453392401E-2,7.7803840526546347E-2,7.6358509536739116E-2,7.4933699534327061E-2,7.3529259609648373E-2,7.2145036965893777E-2,7.0780876991685518E-2,6.9436623333331698E-2,6.8112117966725436E-2]
[null,-1.3,9.6800484585610316E-2,9.5097917795239018E-2,9.3417508993471773E-2,9.1759135650280807E-2,9.0122672464452463E-2,8.8507991437401998E-2,8.6914961947084993E-2,8.534345082196694E-2,8.3793322415014249E-2,8.2264438677668902E-2]
[null,-1.2,0.11506967022170828,0.11313944644397728,0.11123243744783459,0.1093485524256919,0.1074876970745869,0.10564977366685525,0.10383468112130037,0.1020423150748191,0.10027256795444205,9.8525329049747812E-2]
[null,-1.1000000000000001,0.13566606094638264,0.1334995132427472,0.13135688104273069,0.12923811224001777,0.12714315056279821,0.12507193563715019,0.12302440305134332,0.12100048442101816,0.11900010745520065,0.11702319602310868]
[null,-1,0.15865525393145699,0.15624764502125454,0.15386423037273483,0.15150500278834367,0.1491699503309814,0.14685905637589594,0.14457229966390958,0.14230965435593917,0.14007109008876906,0.13785657203203544]
[null,-0.9,0.1840601253467595,0.18141125489179724,0.17878637961437172,0.1761855422452579,0.17360878033862448,0.17105612630848177,0.16852760746683779,0.16602324606352964,0.16354305932769236,0.16108705951083091]
[null,-0.8,0.21185539858339661,0.2089700878716016,0.20610805358581305,0.20326939182806841,0.20045419326044966,0.19766254312269235,0.19489452125180831,0.19215020210369613,0.18942965477671211,0.18673294303717258]
[null,-0.7,0.24196365222307298,0.23885206808998671,0.23576249777925118,0.23269509230089741,0.22964999716479059,0.22662735237686821,0.22362729243759941,0.22064994634264959,0.21769543758573318,0.21476388416363718]
[null,-0.6,0.27425311775007355,0.27093090378300566,0.267628893468983,0.26434729211567748,0.26108629969286151,0.25784611080586467,0.25462691467133614,0.25142889509531008,0.24825223045357048,0.24509709367430943]
[null,-0.5,0.30853753872598688,0.30502573089751939,0.30153178754696619,0.29805596539487639,0.29459851621569799,0.29115968678834636,0.28773971884902705,0.28433884904632412,0.2809573088985643,0.27759532475346493]
[null,-0.4,0.34457825838967576,0.34090297377232259,0.33724272684824946,0.33359782059545762,0.32996855366059363,0.32635522028791997,0.32275811025034773,0.3191775087825558,0.31561369651622251,0.31206694941739055]
[null,-0.3,0.38208857781104733,0.37828047817798072,0.37448416527667994,0.37069998105934648,0.36692826396397193,0.3631693488243809,0.35942356678200876,0.35569124519945322,0.35197270757583721,0.34826827346401756]
[null,-0.2,0.42074029056089696,0.41683383651755768,0.41293557735178538,0.40904588485799409,0.40516512830220414,0.4012936743170763,0.39743188679823949,0.39358012680196047,0.38973875244420275,0.38590811880112263]
[null,-0.1,0.46017216272297101,0.45620468745768322,0.45224157397941611,0.44828321334543886,0.44432999519409355,0.44038230762975744,0.43644053710856717,0.43250506832496155,0.42857628409909926,0.42465456526520451]
[null,0,0.5,0.4960106436853684,0.492021686283098,0.48803352658588733,0.48404656314716926,0.48006119416162751,0.47607781734589316,0.47209682981947887,0.46811862798601261,0.46414360741482791]

{"sheet":"Z > 0","index":3,"n_rows":35,"n_cols":15,"rows_kept":35,"cut":false,"hidden":false,"merged":[]}
[]
[null,null,null,null,"Area Under The Standard Normal Curve (Z > 0)"]
[null,"Z",0,0.01,0.02,0.03,0.04,0.05,0.06,7.0000000000000007E-2,0.08,0.09]
[null,0,{"$f":"NORMSDIST(B4+$C$3)","v":0.5},{"$f":"NORMSDIST(B4+$D$3)","v":0.5039893563146316},{"$f":"NORMSDIST(B4+$E$3)","v":0.50797831371690205},{"$f":"NORMSDIST(B4+$F$3)","v":0.51196647341411272},{"$f":"NORMSDIST(B4+$G$3)","v":0.51595343685283068},{"$f":"NORMSDIST(B4+$H$3)","v":0.51993880583837249},{"$f":"NORMSDIST(B4+$I$3)","v":0.52392218265410684},{"$f":"NORMSDIST(B4+$J$3)","v":0.52790317018052113},{"$f":"NORMSDIST(B4+$K$3)","v":0.53188137201398744},{"$f":"NORMSDIST(B4+$L$3)","v":0.53585639258517204},null,"Example:  For Z - Score = 1.45"]
[null,0.1,{"$f":"NORMSDIST(B5+$C$3)","v":0.53982783727702899},{"$f":"NORMSDIST(B5+$D$3)","v":0.54379531254231672},{"$f":"NORMSDIST(B5+$E$3)","v":0.54775842602058389},{"$f":"NORMSDIST(B5+$F$3)","v":0.55171678665456114},{"$f":"NORMSDIST(B5+$G$3)","v":0.55567000480590645},{"$f":"NORMSDIST(B5+$H$3)","v":0.5596176923702425},{"$f":"NORMSDIST(B5+$I$3)","v":0.56355946289143288},{"$f":"NORMSDIST(B5+$J$3)","v":0.56749493167503839},{"$f":"NORMSDIST(B5+$K$3)","v":0.5714237159009008},{"$f":"NORMSDIST(B5+$L$3)","v":0.57534543473479549},null,null,"First two digits for Row of 1.4"]
[null,0.2,0.57925970943910299,0.58316616348244232,0.58706442264821468,0.59095411514200591,0.59483487169779581,0.5987063256829237,0.60256811320176051,0.60641987319803947,0.61026124755579725,0.61409188119887737,null,null,"Third digit is for column 0.05"]
[null,0.3,0.61791142218895267,0.62171952182201928,0.62551583472332006,0.62930001894065346,0.63307173603602807,0.6368306511756191,0.64057643321799129,0.64430875480054683,0.64802729242416279,0.65173172653598244,null,null,"The value is = 0.9265"]
[null,0.4,0.65542174161032429,0.65909702622767741,0.66275727315175059,0.66640217940454238,0.67003144633940637,0.67364477971208003,0.67724188974965227,0.6808224912174442,0.68438630348377749,0.68793305058260945]
[null,0.5,0.69146246127401312,0.69497426910248061,0.69846821245303381,0.70194403460512356,0.70540148378430201,0.70884031321165364,0.71226028115097295,0.71566115095367588,0.7190426911014357,0.72240467524653507]
[null,0.6,0.72574688224992645,0.72906909621699434,0.732371106531017,0.73565270788432247,0.73891370030713843,0.74215388919413527,0.74537308532866386,0.74857110490468992,0.75174776954642952,0.75490290632569057]
[null,0.7,0.75803634777692697,0.76114793191001329,0.76423750222074882,0.76730490769910253,0.77035000283520938,0.77337264762313174,0.77637270756240062,0.77935005365735044,0.78230456241426682,0.78523611583636277]
[null,0.8,0.78814460141660336,0.79102991212839835,0.79389194641418692,0.79673060817193164,0.79954580673955034,0.80233745687730762,0.80510547874819172,0.80784979789630385,0.81057034522328786,0.81326705696282742]
[null,0.9,0.81593987465324047,0.81858874510820279,0.82121362038562828,0.82381445775474216,0.82639121966137552,0.82894387369151823,0.83147239253316219,0.83397675393647042,0.83645694067230769,0.83891294048916909]
[null,1,0.84134474606854304,0.84375235497874546,0.84613576962726511,0.84849499721165633,0.85083004966901865,0.85314094362410409,0.85542770033609039,0.85769034564406077,0.85992890991123094,0.8621434279679645]
[null,1.1000000000000001,0.86433393905361733,0.86650048675725277,0.86864311895726931,0.8707618877599822,0.87285684943720176,0.87492806436284987,0.87697559694865668,0.87899951557898182,0.88099989254479938,0.88297680397689127]
[null,1.2,0.88493032977829178,0.88686055355602278,0.88876756255216538,0.89065144757430814,0.89251230292541306,0.89435022633314476,0.89616531887869966,0.89795768492518091,0.89972743204555794,0.90147467095025213]
[null,1.3,0.9031995154143897,0.90490208220476098,0.90658249100652821,0.90824086434971918,0.90987732753554751,0.91149200856259804,0.91308503805291497,0.91465654917803307,0.91620667758498575,0.91773556132233114]
[null,1.4,0.91924334076622893,0.92073015854660756,0.92219615947345368,0.92364149046326083,0.92506630046567295,0.9264707403903516,0.92785496303410619,0.92921912300831444,0.93056337666666833,0.93188788203327455]
[null,1.5,0.93319279873114191,0.93447828791108356,0.93574451218106425,0.93699163553602161,0.93821982328818809,0.93942924199794098,0.94062005940520699,0.94179244436144693,0.94294656676224586,0.94408259748053058]
[null,1.6,0.94520070830044201,0.94630107185188028,0.94738386154574794,0.94844925150991066,0.94949741652589625,0.9505285319663519,0.95154277373327723,0.95254031819705265,0.95352134213628004,0.95448602267845017]
[null,1.7,0.95543453724145699,0.95636706347596812,0.95728377920867114,0.9581848623864051,0.95907049102119268,0.95994084313618289,0.96079609671251731,0.96163642963712881,0.96246201965148326,0.9632730443012737]
[null,1.8,0.96406968088707423,0.9648521064159612,0.96562049755411006,0.96637503058037166,0.96711588134083615,0.96784322520438626,0.96855723701924734,0.96925809107053407,0.96994596103880026,0.9706210199595906]
[null,1.9,0.97128344018399815,0.97193339334022744,0.9725710502961632,0.97319658112294505,0.97381015505954727,0.97441194047836144,0.97500210485177952,0.97558081471977742,0.97614823565849151,0.97670453224978815]
[null,2,0.97724986805182079,0.97778440557056856,0.97830830623235321,0.97882173035732778,0.97932483713392993,0.97981778459429558,0.98030072959062309,0.98077382777248268,0.98123723356506221,0.98169110014834104]
[null,2.1,0.98213557943718344,0.98257082206234292,0.98299697735236724,0.98341419331639501,0.98382261662783388,0.98422239260890954,0.98461366521607452,0.98499657702626775,0.98537126922401075,0.98573788158933118]
[null,2.2000000000000002,0.98609655248650141,0.98644741885358,0.98679061619274377,0.98712627856139801,0.98745453856405341,0.98777552734495533,0.98808937458145296,0.98839620847809651,0.9886961557614472,0.98898934167558861]
[null,2.2999999999999998,0.98927588997832416,0.98955592293804895,0.98982956133128031,0.99009692444083575,0.99035813005464168,0.99061329446516144,0.99086253246942735,0.99110595736966323,0.99134368097448344,0.99157581360065428]
[null,2.4,0.99180246407540384,0.99202373973926627,0.99223974644944635,0.99245058858369084,0.99265636904465171,0.99285718926472855,0.99305314921137566,0.99324434739285938,0.99343088086445319,0.99361284523505677]
[null,2.5,0.99379033467422384,0.9939634419195873,0.99413225828466745,0.99429687366704933,0.99445737655691735,0.99461385404593328,0.99476639183644422,0.994915074251009,0.99505998424222941,0.99520120340287377]
[null,2.6,0.99533881197628127,0.99547288886703267,0.99560351165187866,0.9957307565909107,0.99585469863896392,0.99597541145724167,0.99609296742514719,0.99620743765231456,0.99631889199082502,0.99642739904760025]
[null,2.7,0.99653302619695938,0.9966358395933308,0.99673590418410873,0.99683328372264224,0.99692804078134956,0.99702023676494544,0.99710993192377384,0.99719718536723501,0.99728205507729872,0.99736459792209509]
[null,2.8,0.99744486966957202,0.99752292500121409,0.9975988175258107,0.9976725997932685,0.99774432330845764,0.99781403854508677,0.99788179495959539,0.99794764100506028,0.99801162414510569,0.99807379086781212]
[null,2.9,0.99813418669961596,0.99819285621919351,0.99824984307132392,0.99830518998072271,0.99835893876584303,0.99841113035263518,0.99846180478826196,0.99851100125476255,0.99855875808266004,0.9986051127645077]
[null,3,0.9986501019683699,0.99869376155123057,0.99873612657232769,0.99877723130640772,0.9988171092568956,0.99885579316897732,0.99889331504259071,0.99892970614532106,0.99896499702519714,0.99899921752338594]
[null,3.1,0.99903239678678168,0.99906456328048587,0.99909574480017771,0.99912596848436841,0.99915526082654138,0.99918364768717138,0.99921115430562446,0.99923780531193274,0.9992636247384461,0.99928863603135465]

{"sheet":"Background","index":4,"n_rows":57,"n_cols":23,"rows_kept":57,"cut":false,"hidden":true,"merged":[]}
[]
[null,null,"Hint 1:","Straight Average VS Weighted Average:",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"The Variance: \n",null,null," Standard Seviation"]
[null,null,null,"  Weighted Average =  average where each value has a specific weight or frequency "]
[null,null,null,"       Example: The following were 5 different Unit Prices in 11 projects distubuted as:",null,null,null,null,null,null,null,null,null,null,null,null,null,null,"  They are measures of how  spread out a distribution is."]
[null,null,null,null," =","100, 90, 90, 85, 80, 80, 75, 75, 75, 75, 75",null,null,null,null,null,null,null,null,null,null,null,null,"   In other words, they are measures of variability."]
[null,null,null,null," =",11]
[null,null,null,"              Straight (normal) Average:  (100 + 90 + 85 + 80 + 75)/ 5 = 86",null,null,null,null,null,null,null,null,null,null,null,null,null,null,"σ : Population standard deviation (n > 30) "]
[null,null,null,"              Weighted Average:  (100x1 + 90 x2 + 85x1 + 80x2 + 75x5) / 11 = 81.82"]
[]
[null,null,null," Median: is the middle point , in which half the numbers are above the median and half are below."]
[null,null,null,"              Median of the prices above is = 80 (5 above and 5 below)",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Weighted Average  of a population"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"The population Number "]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Excel Formula to find σ     =STDEV.P"]
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[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"s: Sample standard deviation  (n < 30)"]
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[]
[]
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[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Weighted Average of a sample"]
[null,null,null,null,null,"Left, negatively skewed ",null,null,null,"Symmetric",null,null,"Right, positively skewed ",null,null,null,null,null,null,null,"The population Number "]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Excel Formula to find s     =STDEV.S"]
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[null,null,"Hint 2:","Limit: Confidence Interval",null,null,null,null,null,null,null,"Formulas Used"]
[null,null,null,"Common level of confidence Interval = 95%",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Standard Normal Distribution, Z- table"]
[null,null,null,null,null,null,null,null,null,null,null,null,"Number of record, n > 30 ",null,null,null,null,null,null,"For  Prob = 47.5% (covering 95% total),    Z-score is = 1.96"]
[]
[]
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[null,null,null,null,null,null,null,null,null,null,"Using the Z table."]
[null,null,null,null,null,null,null,null,null,null,"Standard Normal Distribution"]
[null,null,null,null,null,null,null,null,null,null," σ: Population standard deviation. "]
[]
[null,null,null,"Example:",null,null,null,null,null,null,"Example 1: For 95% Confidence interval:"]
[null,null,null,"If the weighted average is $70, and the 95% confidence level = $68 -  $74",null,null,null,null,null,null,null,"Prob =  47.5% on each side, Borders:  2.5%"]
[null,null,null,"Then, 95% of prices should be within that limit or between $68 and $74",null,null,null,null,null,null,null,"Or: Z = 1.96 for 0.4750, 47.5% from table"]
[null,null,null,"   (47.5% below and 47.5% above the weighted average)"]
[]
[]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"* Excel uses the border values in the formula"]
[null,null,null,null,null,null,null,null,null,null,"Example 2: For 30% Confidence interval:",null,null,null,null,null,null,null,null,"      For 95%, then the borders are (1-0.95)/2 = 0.025"]
[null,null,null,null,null,null,null,null,null,null,null,"Prob =  15% on each side, Borders: 35%",null,null,null,null,null,null,null,"      The other border is (1 - 0.025) = 0.9750"]
[null,null,null,null,null,null,null,null,null,null,null,"Or: Z = approx. 0.385 from table",null,null,null,null,null,null,null,null,"=NORMSINV(0.025)= -1.95996 = -1.96"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"=NORMSINV(0.975) = 1.95996 = 1.96"]
[null,null,null,null,null,null,null,null,null,null,"* Excel Formula to find Z for 95%:     =NORMSINV(0.025)"]
[null,null,null,"Optional: By selecting any range such as 30%",null,null,null,null,null,null,null,null,"Number of record, n < 30 "]
[null,null,null,"If the prices are: $69 - $72 within the 30% range,  then:"]
[]
[]
[]
[null,null,null,null,null,null,null,null,null,null,"Using the t table with Degrees of Freedom  df = n - 1."]
[null,null,null,null,null,null,null,null,null,null,"t distribution (Student's distribution)"]
[null,null,null,null,null,null,null,null,null,null,"s: Sample standard deviation."]
[null,null,null,null,null,null,null,null,null,null,"For 95% Confidence interval, Prob = 0.05 for 2 tailed (used)"]
[null,null,null,null,null,null,null,null,null,null,"For 95% Confidence interval, Prob = 0.025 for 1 tailed"]
[null,null,null,"                     (15% below and 15% above the weighted average)",null,null,null,null,null,null,"Excel Formula to find t for 95%:   = TINV(0.05, df)"]

{"sheet":"Forecast","index":5,"n_rows":70,"n_cols":2,"rows_kept":70,"cut":false,"hidden":true,"merged":[]}
["                  Note; The following is advance statistical analysis for information only"]
[]
[null,"Confidence and prediction intervals for forecasted values"]
[null,"http://www.real-statistics.com/regression/confidence-and-prediction-intervals/"]
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[null,"The 95% confidence interval for the forecasted values ŷ of x is"]
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[null,"                where"]
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[null,"This means that there is a 95% probability that the true linear regression line of the population will lie within the confidence interval of the regression line calculated from the sample data."]
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[null,"Figure 1 – Confidence vs. prediction intervals"]
[null,"In the graph on the left , a linear regression line is calculated to fit the sample data points. The confidence interval consists of the space between the two curves (dotted lines). Thus there is a 95% probability that the true best-fit line for the population lies within the confidence interval (e.g. any of the lines in the figure on the right above)."]
[null,"There is also a concept called prediction interval. Here we look at any specific value of x, x0, and find an interval around the predicted value ŷ0 for x0 such that there is a 95% probability that the real value of y (in the population) corresponding to x0 is within this interval (see the graph on the right side of Figure 1)."]
[null,"The 95% prediction interval of the forecasted value ŷ0 for x0 is"]
[]
[null,"where the standard error of the prediction is"]
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[null,"For any specific value x0 the prediction interval is more meaningful than the confidence interval."]
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[null,"Example 1: Find the 95% confidence and prediction intervals for the forecasted life expectancy for men who smoke 20 cigarettes in Example 1 of Method of Least Squares."]
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[null,"Figure 2 – Confidence and prediction intervals"]
[null,"Referring to Figure 2, we see that the forecasted value for 20 cigarettes is given by FORECAST(20,B4:B18,A4:A18) = 73.16. The confidence interval, calculated using the standard error 2.06 (found in cell E12), is (68.70, 77.61)."]
[]
[null,"The prediction interval is calculated in a similar way using the prediction standard error of 8.24 (found in cell J12). Thus life expectancy of men who smoke 20 cigarettes is in the interval (55.36, 90.95) with 95% probability."]
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[null,"Example 2: Test whether the y-intercept is 0."]
[null,"We use the same approach as that used in Example 1 to find the confidence interval of ŷ when x = 0 (this is the y-intercept). The result is given in column M of Figure 2. Here the standard error is"]
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[null,"and so the confidence interval is"]
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[null,"Since 0 is not in this interval, the null hypothesis that the y-intercept is zero is rejected."]