{"text_format":"3","workbook":"xlsx","n_sheets":4,"sheets":["prob","Sheet2","Sheet3","Sheet4"],"not_rendered":{"charts":1,"images":4,"macros":1,"defined_names":6,"comments":1},"read":"whole","date_system":"1900"}

{"sheet":"prob","index":0,"n_rows":856,"n_cols":22,"rows_kept":856}
[null,null,"   The Standard Deviations"]
[null,null," of the Sample Proportions"]
[]
[null,"    This program investigates the spread in the"]
[null,"sample proportions based on repeated samples"]
[null,"from a population with probability of success p"]
[]
["What is the probability of success p?",null,null,{"$f":"E8/100","v":0.5},50]
[]
["What is the sample size n (1-100)?",null,null,10]
[]
["How many random samples (100-1000)?",null,null,100]
[]
[]
[{"$f":"\"For the \"&TEXT(flips,\"000\")&\" samples from this population:\"","v":"For the 100 samples from this population:"}]
[null,"The average standard deviation",{"$nulls":6},"By theory, the mean and standard deviation are:"]
[null,null,{"$f":"\"       of the \"&TEXT(flips,\"0\")& \" sample proportions =\"","v":"       of the 100 sample proportions ="},null,{"$f":"SUM(Sheet2!B2:B1002)/flips","v":{"v":1.5038981757199528,"d":"1.504"}},{"$nulls":5},"  m =   ",{"$f":"p","v":0.5}]
[{"$nulls":10},"  s =",{"$f":"Sheet2!K3","v":{"v":0.15811388300841897,"d":"0.158"}}]
[]
[]
[]
[{"$nulls":3},-1,{"$nulls":6},{"$f":"Sheet2!H28","v":1.5038981757199528},{"$f":"Sheet2!I28","v":0.27969999999999984}]
[]
[]
["Click each item below for suggestions and investigations"]
[null,null,"   Item 1"]
[null,null,"   Item 2"]
[null,null,"   Item 3"]
[null,null,"   Item 4"]
[null,null,"   Item 5"]
[null,null,"   Item 6"]
[]
[]
[]
["To access/download all the DIGMath Apps for Statistics"]
["Click this link:",null,"DIGMath for Statistics and Probability"]
[]
["Created by:  Sheldon P. Gordon   &   Florence S. Gordon"]
["                  Farmingdale State College      NYIT"]
["Development of this module was supported by the "]
["NSF's Division of Undergraduate Education  "]
["under grants DUE-0310123 and DUE-0442160."]
{"$rows_empty":813}
[{"$nulls":20},{"$f":"Sheet2!B856","v":""},{"$f":"Sheet2!B856","v":""}]

{"sheet":"Sheet2","index":1,"n_rows":1001,"n_cols":13,"rows_kept":1001}
[null,"sampsd",null,"sample p","sample pp^2","sample sd"]
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[2,{"$f":"IF(A3<=flips,sampsd(trials,p,NewSample),\"\")","v":{"v":1.5491933384829668,"d":"1.549"}},2.4000000000000004,{"$f":"IF($A3<=flips,props(trials,p,NewSample),\"\")","v":{"v":0.4,"d":"0.400"}},{"v":0.16000000000000003,"d":"0.160"},null,0,{"$f":"COUNTIF(B$2:B$1001,\"<0.25\")","v":0},{"$f":"p","v":0.5},"s=",{"$f":"SQRT(p*(1-p)/trials)","v":0.15811388300841897}]
[3,{"$f":"IF(A4<=flips,sampsd(trials,p,NewSample),\"\")","v":{"v":1.5811388300841898,"d":"1.581"}},2.5000000000000004,{"$f":"IF($A4<=flips,props(trials,p,NewSample),\"\")","v":{"v":0.5,"d":"0.500"}},{"v":0.25,"d":"0.250"},null,0.25,{"$f":"COUNTIF(B$2:B$1001,\"<.5\")-H3","v":{"v":0,"d":"0.000"}},0.5,"xbar=",{"$f":"SUM(D2:D1001)/trials","v":{"v":5.070000000000002,"d":"5.07"}}]
[4,{"$f":"IF(A5<=flips,sampsd(trials,p,NewSample),\"\")","v":{"v":1.2649110640673515,"d":"1.265"}},1.5999999999999994,{"$f":"IF($A5<=flips,props(trials,p,NewSample),\"\")","v":{"v":0.4,"d":"0.400"}},{"v":0.16000000000000003,"d":"0.160"},null,{"$f":"G4+0.25","v":0.5},{"$f":"COUNTIF(B$2:B$1001,\"<.75\")-SUM(H$3:H4)","v":{"v":0,"d":"0.000"}},0.5,"sd=",{"$f":"SQRT((SUM(C2:C1001)-2*prob!$E$16*SUM(B2:B1001)+flips*prob!$E$16^2)/(flips-1))","v":{"v":1.5142421513513922,"d":"1.514"}}]
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[7,{"$f":"IF(A8<=flips,sampsd(trials,p,NewSample),\"\")","v":{"v":1.5491933384829668,"d":"1.549"}},2.4000000000000004,{"$f":"IF($A8<=flips,props(trials,p,NewSample),\"\")","v":{"v":0.4,"d":"0.400"}},{"v":0.16000000000000003,"d":"0.160"},null,1.25,{"$f":"COUNTIF(B$2:B$1001,\"<1.5\")-SUM(H$3:H7)","v":{"v":37,"d":"37.000"}},0.5]
[8,{"$f":"IF(A9<=flips,sampsd(trials,p,NewSample),\"\")","v":{"v":1.5491933384829668,"d":"1.549"}},2.4000000000000004,{"$f":"IF($A9<=flips,props(trials,p,NewSample),\"\")","v":{"v":0.5,"d":"0.500"}},{"v":0.25,"d":"0.250"},null,1.5,{"$f":"COUNTIF(B$2:B$1001,\"<1.75\")-SUM(H$3:H8)","v":{"v":63,"d":"63.000"}},0.5]
[9,{"$f":"IF(A10<=flips,sampsd(trials,p,NewSample),\"\")","v":{"v":1.5811388300841898,"d":"1.581"}},2.5000000000000004,{"$f":"IF($A10<=flips,props(trials,p,NewSample),\"\")","v":{"v":0.4,"d":"0.400"}},{"v":0.16000000000000003,"d":"0.160"},null,1.75,{"$f":"COUNTIF(B$2:B$1001,\"<2\")-SUM(H$3:H9)","v":{"v":0,"d":"0.000"}},0.5]
[10,{"$f":"IF(A11<=flips,sampsd(trials,p,NewSample),\"\")","v":{"v":1.5491933384829668,"d":"1.549"}},2.4000000000000004,{"$f":"IF($A11<=flips,props(trials,p,NewSample),\"\")","v":{"v":0.7,"d":"0.700"}},{"v":0.48999999999999994,"d":"0.490"},null,2,{"$f":"COUNTIF(B$2:B$1001,\"<2.25\")-SUM(H$3:H10)","v":{"v":0,"d":"0.000"}},0.5]
[11,{"$f":"IF(A12<=flips,sampsd(trials,p,NewSample),\"\")","v":{"v":1.5811388300841898,"d":"1.581"}},2.5000000000000004,{"$f":"IF($A12<=flips,props(trials,p,NewSample),\"\")","v":{"v":0.5,"d":"0.500"}},{"v":0.25,"d":"0.250"},null,2.25,{"$f":"COUNTIF(B$2:B$1001,\"<2.5\")-SUM(H$3:H11)","v":{"v":0,"d":"0.000"}},0.5]
[12,{"$f":"IF(A13<=flips,sampsd(trials,p,NewSample),\"\")","v":{"v":1.5811388300841898,"d":"1.581"}},2.5000000000000004,{"$f":"IF($A13<=flips,props(trials,p,NewSample),\"\")","v":{"v":0.3,"d":"0.300"}},{"v":0.09,"d":"0.090"},null,2.5,{"$f":"COUNTIF(B$2:B$1001,\"<2.75\")-SUM(H$3:H12)","v":{"v":0,"d":"0.000"}},0.5]
[13,{"$f":"IF(A14<=flips,sampsd(trials,p,NewSample),\"\")","v":{"v":1.5811388300841898,"d":"1.581"}},2.5000000000000004,{"$f":"IF($A14<=flips,props(trials,p,NewSample),\"\")","v":{"v":0.6,"d":"0.600"}},{"v":0.36,"d":"0.360"},null,2.75,{"$f":"COUNTIF(B$2:B$1001,\"<3\")-SUM(H$3:H13)","v":{"v":0,"d":"0.000"}},0.5]
[14,{"$f":"IF(A15<=flips,sampsd(trials,p,NewSample),\"\")","v":{"v":1.4491376746189437,"d":"1.449"}},2.0999999999999996,{"$f":"IF($A15<=flips,props(trials,p,NewSample),\"\")","v":{"v":0.2,"d":"0.200"}},{"v":0.04000000000000001,"d":"0.040"},null,3,{"$f":"COUNTIF(B$2:B$1001,\"<3.25\")-SUM(H$3:H14)","v":{"v":0,"d":"0.000"}},0.5]
[15,{"$f":"IF(A16<=flips,sampsd(trials,p,NewSample),\"\")","v":{"v":1.5811388300841898,"d":"1.581"}},2.5000000000000004,{"$f":"IF($A16<=flips,props(trials,p,NewSample),\"\")","v":{"v":0.5,"d":"0.500"}},{"v":0.25,"d":"0.250"},null,3.25,{"$f":"COUNTIF(B$2:B$1001,\"<3.5\")-SUM(H$3:H15)","v":{"v":0,"d":"0.000"}},0.5]
[16,{"$f":"IF(A17<=flips,sampsd(trials,p,NewSample),\"\")","v":{"v":1.5491933384829668,"d":"1.549"}},2.4000000000000004,{"$f":"IF($A17<=flips,props(trials,p,NewSample),\"\")","v":{"v":0.5,"d":"0.500"}},{"v":0.25,"d":"0.250"},null,3.5,{"$f":"COUNTIF(B$2:B$1001,\"<3.75\")-SUM(H$3:H16)","v":{"v":0,"d":"0.000"}},0.5]
[17,{"$f":"IF(A18<=flips,sampsd(trials,p,NewSample),\"\")","v":{"v":1.4491376746189437,"d":"1.449"}},2.0999999999999996,{"$f":"IF($A18<=flips,props(trials,p,NewSample),\"\")","v":{"v":0.6,"d":"0.600"}},{"v":0.36,"d":"0.360"},null,3.75,{"$f":"COUNTIF(B$2:B$1001,\"<4\")-SUM(H$3:H17)","v":{"v":0,"d":"0.000"}},0.5]
[18,{"$f":"IF(A19<=flips,sampsd(trials,p,NewSample),\"\")","v":{"v":1.449137674618944,"d":"1.449"}},2.1,{"$f":"IF($A19<=flips,props(trials,p,NewSample),\"\")","v":{"v":0.4,"d":"0.400"}},{"v":0.16000000000000003,"d":"0.160"},null,4,{"$f":"COUNTIF(B$2:B$1001,\"<4.25\")-SUM(H$3:H18)","v":{"v":0,"d":"0.000"}},0.5]
[19,{"$f":"IF(A20<=flips,sampsd(trials,p,NewSample),\"\")","v":{"v":1.5491933384829668,"d":"1.549"}},2.4000000000000004,{"$f":"IF($A20<=flips,props(trials,p,NewSample),\"\")","v":{"v":0.3,"d":"0.300"}},{"v":0.09,"d":"0.090"},null,4.25,{"$f":"COUNTIF(B$2:B$1001,\"<4.5\")-SUM(H$3:H19)","v":{"v":0,"d":"0.000"}},0.5]
[20,{"$f":"IF(A21<=flips,sampsd(trials,p,NewSample),\"\")","v":{"v":1.4491376746189437,"d":"1.449"}},2.0999999999999996,{"$f":"IF($A21<=flips,props(trials,p,NewSample),\"\")","v":{"v":0.4,"d":"0.400"}},{"v":0.16000000000000003,"d":"0.160"},null,4.5,{"$f":"COUNTIF(B$2:B$1001,\"<4.75\")-SUM(H$3:H20)","v":{"v":0,"d":"0.000"}},0.5]
[21,{"$f":"IF(A22<=flips,sampsd(trials,p,NewSample),\"\")","v":{"v":1.449137674618944,"d":"1.449"}},2.1,{"$f":"IF($A22<=flips,props(trials,p,NewSample),\"\")","v":{"v":0.5,"d":"0.500"}},{"v":0.25,"d":"0.250"},null,4.75,{"$f":"COUNTIF(B$2:B$1001,\"<5\")-SUM(H$3:H21)","v":{"v":0,"d":"0.000"}},0.5]
[22,{"$f":"IF(A23<=flips,sampsd(trials,p,NewSample),\"\")","v":{"v":1.4491376746189437,"d":"1.449"}},2.0999999999999996,{"$f":"IF($A23<=flips,props(trials,p,NewSample),\"\")","v":{"v":0.5,"d":"0.500"}},{"v":0.25,"d":"0.250"},null,5]
[23,{"$f":"IF(A24<=flips,sampsd(trials,p,NewSample),\"\")","v":{"v":1.5811388300841898,"d":"1.581"}},2.5000000000000004,{"$f":"IF($A24<=flips,props(trials,p,NewSample),\"\")","v":{"v":0.5,"d":"0.500"}},{"v":0.25,"d":"0.250"}]
[24,{"$f":"IF(A25<=flips,sampsd(trials,p,NewSample),\"\")","v":{"v":1.5811388300841898,"d":"1.581"}},2.5000000000000004,{"$f":"IF($A25<=flips,props(trials,p,NewSample),\"\")","v":{"v":0.4,"d":"0.400"}},{"v":0.16000000000000003,"d":"0.160"}]
[25,{"$f":"IF(A26<=flips,sampsd(trials,p,NewSample),\"\")","v":{"v":1.5491933384829668,"d":"1.549"}},2.4000000000000004,{"$f":"IF($A26<=flips,props(trials,p,NewSample),\"\")","v":{"v":0.6,"d":"0.600"}},{"v":0.36,"d":"0.360"},{"$nulls":5},"      New Sample =",null,{"$f":"prob!D22","v":-1}]
[26,{"$f":"IF(A27<=flips,sampsd(trials,p,NewSample),\"\")","v":{"v":1.5491933384829668,"d":"1.549"}},2.4000000000000004,{"$f":"IF($A27<=flips,props(trials,p,NewSample),\"\")","v":{"v":0.5,"d":"0.500"}},{"v":0.25,"d":"0.250"}]
[27,{"$f":"IF(A28<=flips,sampsd(trials,p,NewSample),\"\")","v":{"v":1.4491376746189437,"d":"1.449"}},2.0999999999999996,{"$f":"IF($A28<=flips,props(trials,p,NewSample),\"\")","v":{"v":0.6,"d":"0.600"}},{"v":0.36,"d":"0.360"},null,null,{"$f":"AVERAGE(B2:B1001)","v":{"v":1.5038981757199528,"d":"1.504"}},{"$f":"AVERAGE(E2:E1001)","v":{"v":0.27969999999999984,"d":"0.280"}}]
[28,{"$f":"IF(A29<=flips,sampsd(trials,p,NewSample),\"\")","v":{"v":1.5811388300841898,"d":"1.581"}},2.5000000000000004,{"$f":"IF($A29<=flips,props(trials,p,NewSample),\"\")","v":{"v":0.5,"d":"0.500"}},{"v":0.25,"d":"0.250"}]
[29,{"$f":"IF(A30<=flips,sampsd(trials,p,NewSample),\"\")","v":{"v":1.449137674618944,"d":"1.449"}},2.1,{"$f":"IF($A30<=flips,props(trials,p,NewSample),\"\")","v":{"v":0.5,"d":"0.500"}},{"v":0.25,"d":"0.250"}]
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[32,{"$f":"IF(A33<=flips,sampsd(trials,p,NewSample),\"\")","v":{"v":1.5491933384829668,"d":"1.549"}},2.4000000000000004,{"$f":"IF($A33<=flips,props(trials,p,NewSample),\"\")","v":{"v":0.7,"d":"0.700"}},{"v":0.48999999999999994,"d":"0.490"}]
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[34,{"$f":"IF(A35<=flips,sampsd(trials,p,NewSample),\"\")","v":{"v":1.2649110640673518,"d":"1.265"}},1.6,{"$f":"IF($A35<=flips,props(trials,p,NewSample),\"\")","v":{"v":0.8,"d":"0.800"}},{"v":0.6400000000000001,"d":"0.640"}]
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[43,{"$f":"IF(A44<=flips,sampsd(trials,p,NewSample),\"\")","v":{"v":1.4491376746189437,"d":"1.449"}},2.0999999999999996,{"$f":"IF($A44<=flips,props(trials,p,NewSample),\"\")","v":{"v":0.7,"d":"0.700"}},{"v":0.48999999999999994,"d":"0.490"}]
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[45,{"$f":"IF(A46<=flips,sampsd(trials,p,NewSample),\"\")","v":{"v":1.449137674618944,"d":"1.449"}},2.1,{"$f":"IF($A46<=flips,props(trials,p,NewSample),\"\")","v":{"v":0.6,"d":"0.600"}},{"v":0.36,"d":"0.360"}]
[46,{"$f":"IF(A47<=flips,sampsd(trials,p,NewSample),\"\")","v":{"v":1.5811388300841898,"d":"1.581"}},2.5000000000000004,{"$f":"IF($A47<=flips,props(trials,p,NewSample),\"\")","v":{"v":0.6,"d":"0.600"}},{"v":0.36,"d":"0.360"}]
[47,{"$f":"IF(A48<=flips,sampsd(trials,p,NewSample),\"\")","v":{"v":1.2649110640673515,"d":"1.265"}},1.5999999999999994,{"$f":"IF($A48<=flips,props(trials,p,NewSample),\"\")","v":{"v":0.3,"d":"0.300"}},{"v":0.09,"d":"0.090"}]
[48,{"$f":"IF(A49<=flips,sampsd(trials,p,NewSample),\"\")","v":{"v":1.5811388300841898,"d":"1.581"}},2.5000000000000004,{"$f":"IF($A49<=flips,props(trials,p,NewSample),\"\")","v":{"v":0.8,"d":"0.800"}},{"v":0.6400000000000001,"d":"0.640"}]
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