$normval=array();
$normval["0.01"]=0.003989;
$normval["0.02"]=0.007978;
$normval["0.03"]=0.011966;
$normval["0.04"]=0.015953;
$normval["0.05"]=0.019939;
$normval["0.06"]=0.023922;
$normval["0.07"]=0.027903;
$normval["0.08"]=0.031881;
$normval["0.09"]=0.035856;
$normval["0.10"]=0.039828;
$normval["0.11"]=0.043795;
$normval["0.12"]=0.047758;
$normval["0.13"]=0.051717;
$normval["0.14"]=0.05567;
$normval["0.15"]=0.059618;
$normval["0.16"]=0.063559;
$normval["0.17"]=0.067495;
$normval["0.18"]=0.071424;
$normval["0.19"]=0.075345;
$normval["0.20"]=0.07926;
$normval["0.21"]=0.083166;
$normval["0.22"]=0.087064;
$normval["0.23"]=0.090954;
$normval["0.24"]=0.094835;
$normval["0.25"]=0.098706;
$normval["0.26"]=0.102568;
$normval["0.27"]=0.10642;
$normval["0.28"]=0.110261;
$normval["0.29"]=0.114092;
$normval["0.30"]=0.117911;
$normval["0.31"]=0.12172;
$normval["0.32"]=0.125516;
$normval["0.33"]=0.1293;
$normval["0.34"]=0.133072;
$normval["0.35"]=0.136831;
$normval["0.36"]=0.140576;
$normval["0.37"]=0.144309;
$normval["0.38"]=0.148027;
$normval["0.39"]=0.151732;
$normval["0.40"]=0.155422;
$normval["0.41"]=0.159097;
$normval["0.42"]=0.162757;
$normval["0.43"]=0.166402;
$normval["0.44"]=0.170031;
$normval["0.45"]=0.173645;
$normval["0.46"]=0.177242;
$normval["0.47"]=0.180822;
$normval["0.48"]=0.184386;
$normval["0.49"]=0.187933;
$normval["0.50"]=0.191462;
$normval["0.51"]=0.194974;
$normval["0.52"]=0.198468;
$normval["0.53"]=0.201944;
$normval["0.54"]=0.205401;
$normval["0.55"]=0.20884;
$normval["0.56"]=0.21226;
$normval["0.57"]=0.215661;
$normval["0.58"]=0.219043;
$normval["0.59"]=0.222405;
$normval["0.60"]=0.225747;
$normval["0.61"]=0.229069;
$normval["0.62"]=0.232371;
$normval["0.63"]=0.235653;
$normval["0.64"]=0.238914;
$normval["0.65"]=0.242154;
$normval["0.66"]=0.245373;
$normval["0.67"]=0.248571;
$normval["0.68"]=0.251748;
$normval["0.69"]=0.254903;
$normval["0.70"]=0.258036;
$normval["0.71"]=0.261148;
$normval["0.72"]=0.264238;
$normval["0.73"]=0.267305;
$normval["0.74"]=0.27035;
$normval["0.75"]=0.273373;
$normval["0.76"]=0.276373;
$normval["0.77"]=0.27935;
$normval["0.78"]=0.282305;
$normval["0.79"]=0.285236;
$normval["0.80"]=0.288145;
$normval["0.81"]=0.29103;
$normval["0.82"]=0.293892;
$normval["0.83"]=0.296731;
$normval["0.84"]=0.299546;
$normval["0.85"]=0.302337;
$normval["0.86"]=0.305105;
$normval["0.87"]=0.30785;
$normval["0.88"]=0.31057;
$normval["0.89"]=0.313267;
$normval["0.90"]=0.31594;
$normval["0.91"]=0.318589;
$normval["0.92"]=0.321214;
$normval["0.93"]=0.323814;
$normval["0.94"]=0.326391;
$normval["0.95"]=0.328944;
$normval["0.96"]=0.331472;
$normval["0.97"]=0.333977;
$normval["0.98"]=0.336457;
$normval["0.99"]=0.338913;
$normval["1.00"]=0.341345;
$normval["1.01"]=0.343752;
$normval["1.02"]=0.346136;
$normval["1.03"]=0.348495;
$normval["1.04"]=0.35083;
$normval["1.05"]=0.353141;
$normval["1.06"]=0.355428;
$normval["1.07"]=0.35769;
$normval["1.08"]=0.359929;
$normval["1.09"]=0.362143;
$normval["1.10"]=0.364334;
$normval["1.11"]=0.3665;
$normval["1.12"]=0.368643;
$normval["1.13"]=0.370762;
$normval["1.14"]=0.372857;
$normval["1.15"]=0.374928;
$normval["1.16"]=0.376976;
$normval["1.17"]=0.379;
$normval["1.18"]=0.381;
$normval["1.19"]=0.382977;
$normval["1.20"]=0.38493;
$normval["1.21"]=0.386861;
$normval["1.22"]=0.388768;
$normval["1.23"]=0.390651;
$normval["1.24"]=0.392512;
$normval["1.25"]=0.39435;
$normval["1.26"]=0.396165;
$normval["1.27"]=0.397958;
$normval["1.28"]=0.399727;
$normval["1.29"]=0.401475;
$normval["1.30"]=0.4032;
$normval["1.31"]=0.404902;
$normval["1.32"]=0.406582;
$normval["1.33"]=0.408241;
$normval["1.34"]=0.409877;
$normval["1.35"]=0.411492;
$normval["1.36"]=0.413085;
$normval["1.37"]=0.414657;
$normval["1.38"]=0.416207;
$normval["1.39"]=0.417736;
$normval["1.40"]=0.419243;
$normval["1.41"]=0.42073;
$normval["1.42"]=0.422196;
$normval["1.43"]=0.423641;
$normval["1.44"]=0.425066;
$normval["1.45"]=0.426471;
$normval["1.46"]=0.427855;
$normval["1.47"]=0.429219;
$normval["1.48"]=0.430563;
$normval["1.49"]=0.431888;
$normval["1.50"]=0.433193;
$normval["1.51"]=0.434478;
$normval["1.52"]=0.435745;
$normval["1.53"]=0.436992;
$normval["1.54"]=0.43822;
$normval["1.55"]=0.439429;
$normval["1.56"]=0.44062;
$normval["1.57"]=0.441792;
$normval["1.58"]=0.442947;
$normval["1.59"]=0.444083;
$normval["1.60"]=0.445201;
$normval["1.61"]=0.446301;
$normval["1.62"]=0.447384;
$normval["1.63"]=0.448449;
$normval["1.64"]=0.449497;
$normval["1.65"]=0.450529;
$normval["1.66"]=0.451543;
$normval["1.67"]=0.45254;
$normval["1.68"]=0.453521;
$normval["1.69"]=0.454486;
$normval["1.70"]=0.455435;
$normval["1.71"]=0.456367;
$normval["1.72"]=0.457284;
$normval["1.73"]=0.458185;
$normval["1.74"]=0.45907;
$normval["1.75"]=0.459941;
$normval["1.76"]=0.460796;
$normval["1.77"]=0.461636;
$normval["1.78"]=0.462462;
$normval["1.79"]=0.463273;
$normval["1.80"]=0.46407;
$normval["1.81"]=0.464852;
$normval["1.82"]=0.46562;
$normval["1.83"]=0.466375;
$normval["1.84"]=0.467116;
$normval["1.85"]=0.467843;
$normval["1.86"]=0.468557;
$normval["1.87"]=0.469258;
$normval["1.88"]=0.469946;
$normval["1.89"]=0.470621;
$normval["1.90"]=0.471283;
$normval["1.91"]=0.471933;
$normval["1.92"]=0.472571;
$normval["1.93"]=0.473197;
$normval["1.94"]=0.47381;
$normval["1.95"]=0.474412;
$normval["1.96"]=0.475002;
$normval["1.97"]=0.475581;
$normval["1.98"]=0.476148;
$normval["1.99"]=0.476705;
$normval["2.00"]=0.47725;
$normval["2.01"]=0.477784;
$normval["2.02"]=0.478308;
$normval["2.03"]=0.478822;
$normval["2.04"]=0.479325;
$normval["2.05"]=0.479818;
$normval["2.06"]=0.480301;
$normval["2.07"]=0.480774;
$normval["2.08"]=0.481237;
$normval["2.09"]=0.481691;
$normval["2.10"]=0.482136;
$normval["2.11"]=0.482571;
$normval["2.12"]=0.482997;
$normval["2.13"]=0.483414;
$normval["2.14"]=0.483823;
$normval["2.15"]=0.484222;
$normval["2.16"]=0.484614;
$normval["2.17"]=0.484997;
$normval["2.18"]=0.485371;
$normval["2.19"]=0.485738;
$normval["2.20"]=0.486097;
$normval["2.21"]=0.486447;
$normval["2.22"]=0.486791;
$normval["2.23"]=0.487126;
$normval["2.24"]=0.487455;
$normval["2.25"]=0.487776;
$normval["2.26"]=0.488089;
$normval["2.27"]=0.488396;
$normval["2.28"]=0.488696;
$normval["2.29"]=0.488989;
$normval["2.30"]=0.489276;
$normval["2.31"]=0.489556;
$normval["2.32"]=0.48983;
$normval["2.33"]=0.490097;
$normval["2.34"]=0.490358;
$normval["2.35"]=0.490613;
$normval["2.36"]=0.490863;
$normval["2.37"]=0.491106;
$normval["2.38"]=0.491344;
$normval["2.39"]=0.491576;
$normval["2.40"]=0.491802;
$normval["2.41"]=0.492024;
$normval["2.42"]=0.49224;
$normval["2.43"]=0.492451;
$normval["2.44"]=0.492656;
$normval["2.45"]=0.492857;
$normval["2.46"]=0.493053;
$normval["2.47"]=0.493244;
$normval["2.48"]=0.493431;
$normval["2.49"]=0.493613;
$normval["2.50"]=0.49379;
$normval["2.51"]=0.493963;
$normval["2.52"]=0.494132;
$normval["2.53"]=0.494297;
$normval["2.54"]=0.494457;
$normval["2.55"]=0.494614;
$normval["2.56"]=0.494766;
$normval["2.57"]=0.494915;
$normval["2.58"]=0.49506;
$normval["2.59"]=0.495201;
$normval["2.60"]=0.495339;
$normval["2.61"]=0.495473;
$normval["2.62"]=0.495604;
$normval["2.63"]=0.495731;
$normval["2.64"]=0.495855;
$normval["2.65"]=0.495975;
$normval["2.66"]=0.496093;
$normval["2.67"]=0.496207;
$normval["2.68"]=0.496319;
$normval["2.69"]=0.496427;
$normval["2.70"]=0.496533;
$normval["2.71"]=0.496636;
$normval["2.72"]=0.496736;
$normval["2.73"]=0.496833;
$normval["2.74"]=0.496928;
$normval["2.75"]=0.49702;
$normval["2.76"]=0.49711;
$normval["2.77"]=0.497197;
$normval["2.78"]=0.497282;
$normval["2.79"]=0.497365;
$normval["2.80"]=0.497445;
$normval["2.81"]=0.497523;
$normval["2.82"]=0.497599;
$normval["2.83"]=0.497673;
$normval["2.84"]=0.497744;
$normval["2.85"]=0.497814;
$normval["2.86"]=0.497882;
$normval["2.87"]=0.497948;
$normval["2.88"]=0.498012;
$normval["2.89"]=0.498074;
$normval["2.90"]=0.498134;
$normval["2.91"]=0.498193;
$normval["2.92"]=0.49825;
$normval["2.93"]=0.498305;
$normval["2.94"]=0.498359;
$normval["2.95"]=0.498411;
$normval["2.96"]=0.498462;
$normval["2.97"]=0.498511;
$normval["2.98"]=0.498559;
$normval["2.99"]=0.498605;
$normval["3.00"]=0.49865;
$normval["3.01"]=0.498694;
$normval["3.02"]=0.498736;
$normval["3.03"]=0.498777;
$normval["3.04"]=0.498817;
$normval["3.05"]=0.498856;
$normval["3.06"]=0.498893;
$normval["3.07"]=0.49893;
$normval["3.08"]=0.498965;
$normval["3.09"]=0.498999;
$normval["3.10"]=0.499032;
$normval["3.11"]=0.499065;
$normval["3.12"]=0.499096;
$normval["3.13"]=0.499126;
$normval["3.14"]=0.499155;
$normval["3.15"]=0.499184;
$normval["3.16"]=0.499211;
$normval["3.17"]=0.499238;
$normval["3.18"]=0.499264;
$normval["3.19"]=0.499289;
$normval["3.20"]=0.499313;
$normval["3.21"]=0.499336;
$normval["3.22"]=0.499359;
$normval["3.23"]=0.499381;
$normval["3.24"]=0.499402;
$normval["3.25"]=0.499423;
$normval["3.26"]=0.499443;
$normval["3.27"]=0.499462;
$normval["3.28"]=0.499481;
$normval["3.29"]=0.499499;
$normval["3.30"]=0.499517;
$normval["3.31"]=0.499534;
$normval["3.32"]=0.49955;
$normval["3.33"]=0.499566;
$normval["3.34"]=0.499581;
$normval["3.35"]=0.499596;
$normval["3.36"]=0.49961;
$normval["3.37"]=0.499624;
$normval["3.38"]=0.499638;
$normval["3.39"]=0.499651;
$normval["3.40"]=0.499663;
$normval["3.41"]=0.499675;
$normval["3.42"]=0.499687;
$normval["3.43"]=0.499698;
$normval["3.44"]=0.499709;
$normval["3.45"]=0.49972;
$normval["3.46"]=0.49973;
$normval["3.47"]=0.49974;
$normval["3.48"]=0.499749;
$normval["3.49"]=0.499758;
$normval["3.50"]=0.499767;
$normval["3.51"]=0.499776;
$normval["3.52"]=0.499784;
$normval["3.53"]=0.499792;
$normval["3.54"]=0.4998;
$normval["3.55"]=0.499807;
$normval["3.56"]=0.499815;
$normval["3.57"]=0.499822;
$normval["3.58"]=0.499828;
$normval["3.59"]=0.499835;
$normval["3.60"]=0.499841;
$normval["3.61"]=0.499847;
$normval["3.62"]=0.499853;
$normval["3.63"]=0.499858;
$normval["3.64"]=0.499864;
$normval["3.65"]=0.499869;
$normval["3.66"]=0.499874;
$normval["3.67"]=0.499879;
$normval["3.68"]=0.499883;
$normval["3.69"]=0.499888;
$normval["3.70"]=0.499892;
$normval["3.71"]=0.499896;
$normval["3.72"]=0.4999;
$normval["3.73"]=0.499904;
$normval["3.74"]=0.499908;
$normval["3.75"]=0.499912;
$normval["3.76"]=0.499915;
$normval["3.77"]=0.499918;
$normval["3.78"]=0.499922;
$normval["3.79"]=0.499925;
$normval["3.80"]=0.499928;
$normval["3.81"]=0.499931;
$normval["3.82"]=0.499933;
$normval["3.83"]=0.499936;
$normval["3.84"]=0.499938;
$normval["3.85"]=0.499941;
$normval["3.86"]=0.499943;
$normval["3.87"]=0.499946;
$normval["3.88"]=0.499948;
$normval["3.89"]=0.49995;
$normval["3.90"]=0.499952;
$normval["3.91"]=0.499954;
$normval["3.92"]=0.499956;
$normval["3.93"]=0.499958;
$normval["3.94"]=0.499959;
$normval["3.95"]=0.499961;
$normval["3.96"]=0.499963;
$normval["3.97"]=0.499964;
$normval["3.98"]=0.499966;
$normval["3.99"]=0.499967;
$normval["4.00"]=0.499968;
$normval["4.01"]=0.49997;
$normval["4.02"]=0.499971;
$normval["4.03"]=0.499972;
$normval["4.04"]=0.499973;
$normval["4.05"]=0.499974;
$normval["4.06"]=0.499975;
$normval["4.07"]=0.499976;
$normval["4.08"]=0.499977;
$normval["4.09"]=0.499978;
$normval["4.10"]=0.499979;
$normval["4.11"]=0.49998;
$normval["4.12"]=0.499981;
$normval["4.13"]=0.499982;
$normval["4.14"]=0.499983;
$normval["4.15"]=0.499983;
$normval["4.16"]=0.499984;
$normval["4.17"]=0.499985;
$normval["4.18"]=0.499985;
$normval["4.19"]=0.499986;
$normval["4.20"]=0.499987;
$normval["4.21"]=0.499987;
$normval["4.22"]=0.499988;
$normval["4.23"]=0.499988;
$normval["4.24"]=0.499989;
$normval["4.25"]=0.499989;
$normval["4.26"]=0.49999;
$normval["4.27"]=0.49999;
$normval["4.28"]=0.499991;
$normval["4.29"]=0.499991;
$normval["4.30"]=0.499991;
$normval["4.31"]=0.499992;
$normval["4.32"]=0.499992;
$normval["4.33"]=0.499993;
$normval["4.34"]=0.499993;
$normval["4.35"]=0.499993;
$normval["4.36"]=0.499993;
$normval["4.37"]=0.499994;
$normval["4.38"]=0.499994;
$normval["4.39"]=0.499994;
$normval["4.40"]=0.499995;
$normval["4.41"]=0.499995;
$normval["4.42"]=0.499995;
$normval["4.43"]=0.499995;
$normval["4.44"]=0.499996;
$normval["4.45"]=0.499996;
$normval["4.46"]=0.499996;
$normval["4.47"]=0.499996;
$normval["4.48"]=0.499996;
$normval["4.49"]=0.499996;
$normval["4.50"]=0.499997;
$normval["4.51"]=0.499997;
$normval["4.52"]=0.499997;
$normval["4.53"]=0.499997;
$normval["4.54"]=0.499997;
$normval["4.55"]=0.499997;
$normval["4.56"]=0.499997;
$normval["4.57"]=0.499998;
$normval["4.58"]=0.499998;
$normval["4.59"]=0.499998;
$normval["4.60"]=0.499998;
$normval["4.61"]=0.499998;
$normval["4.62"]=0.499998;
$normval["4.63"]=0.499998;
$normval["4.64"]=0.499998;
$normval["4.65"]=0.499998;
$normval["4.66"]=0.499998;
$normval["4.67"]=0.499998;
$normval["4.68"]=0.499999;
$normval["4.69"]=0.499999;
$normval["4.70"]=0.499999;
$normval["4.71"]=0.499999;
$normval["4.72"]=0.499999;
$normval["4.73"]=0.499999;
$normval["4.74"]=0.499999;
$normval["4.75"]=0.499999;
$normval["4.76"]=0.499999;
$normval["4.77"]=0.499999;
$normval["4.78"]=0.499999;
$normval["4.79"]=0.499999;
$normval["4.80"]=0.499999;
$normval["4.81"]=0.499999;
$normval["4.82"]=0.499999;
$normval["4.83"]=0.499999;
$normval["4.84"]=0.499999;
$normval["4.85"]=0.499999;
$normval["4.86"]=0.499999;
$normval["4.87"]=0.499999;
$normval["4.88"]=0.499999;
$normval["4.89"]=0.499999;
$normval["4.90"]=0.5;
$normval["4.91"]=0.5;
$normval["4.92"]=0.5;
$normval["4.93"]=0.5;
$normval["4.94"]=0.5;
$normval["4.95"]=0.5;
$normval["4.96"]=0.5;
$normval["4.97"]=0.5;
$normval["4.98"]=0.5;
$normval["4.99"]=0.5;
$normval["5.00"]=0.5;
$normval["5.01"]=0.5;
$normval["5.02"]=0.5;
$normval["5.03"]=0.5;
$normval["5.04"]=0.5;
$normval["5.05"]=0.5;
$normval["5.06"]=0.5;
$normval["5.07"]=0.5;
$normval["5.08"]=0.5;
$normval["5.09"]=0.5;
$normval["5.10"]=0.5;
$normval["5.11"]=0.5;
$normval["5.12"]=0.5;
$normval["5.13"]=0.5;
$normval["5.14"]=0.5;
$normval["5.15"]=0.5;
$normval["5.16"]=0.5;
$normval["5.17"]=0.5;
$normval["5.18"]=0.5;
$normval["5.19"]=0.5;
$normval["5.20"]=0.5;
$normval["5.21"]=0.5;
$normval["5.22"]=0.5;
$normval["5.23"]=0.5;
$normval["5.24"]=0.5;
$normval["5.25"]=0.5;
$normval["5.26"]=0.5;
$normval["5.27"]=0.5;
$normval["5.28"]=0.5;
$normval["5.29"]=0.5;
$normval["5.30"]=0.5;
$normval["5.31"]=0.5;
$normval["5.32"]=0.5;
$normval["5.33"]=0.5;
$normval["5.34"]=0.5;
$normval["5.35"]=0.5;
$normval["5.36"]=0.5;
$normval["5.37"]=0.5;
$normval["5.38"]=0.5;
$normval["5.39"]=0.5;
$normval["5.40"]=0.5;
$normval["5.41"]=0.5;
$normval["5.42"]=0.5;
$normval["5.43"]=0.5;
$normval["5.44"]=0.5;
$normval["5.45"]=0.5;
$normval["5.46"]=0.5;
$normval["5.47"]=0.5;
$normval["5.48"]=0.5;
$normval["5.49"]=0.5;
$normval["5.50"]=0.5;
$normval["5.51"]=0.5;
$normval["5.52"]=0.5;
$normval["5.53"]=0.5;
$normval["5.54"]=0.5;
$normval["5.55"]=0.5;
$normval["5.56"]=0.5;
$normval["5.57"]=0.5;
$normval["5.58"]=0.5;
$normval["5.59"]=0.5;
$normval["5.60"]=0.5;
$normval["5.61"]=0.5;
$normval["5.62"]=0.5;
$normval["5.63"]=0.5;
$normval["5.64"]=0.5;
$normval["5.65"]=0.5;
$normval["5.66"]=0.5;
$normval["5.67"]=0.5;
$normval["5.68"]=0.5;
$normval["5.69"]=0.5;
$normval["5.70"]=0.5;
$normval["5.71"]=0.5;
$normval["5.72"]=0.5;
$normval["5.73"]=0.5;
$normval["5.74"]=0.5;
$normval["5.75"]=0.5;
$normval["5.76"]=0.5;
$normval["5.77"]=0.5;
$normval["5.78"]=0.5;
$normval["5.79"]=0.5;
$normval["5.80"]=0.5;
$normval["5.81"]=0.5;
$normval["5.82"]=0.5;
$normval["5.83"]=0.5;
$normval["5.84"]=0.5;
$normval["5.85"]=0.5;
$normval["5.86"]=0.5;
$normval["5.87"]=0.5;
$normval["5.88"]=0.5;
$normval["5.89"]=0.5;
$normval["5.90"]=0.5;
$normval["5.91"]=0.5;
$normval["5.92"]=0.5;
$normval["5.93"]=0.5;
$normval["5.94"]=0.5;
$normval["5.95"]=0.5;
$normval["5.96"]=0.5;
$normval["5.97"]=0.5;
$normval["5.98"]=0.5;
$normval["5.99"]=0.5;
$normval["6.00"]=0.5;
$normval["6.01"]=0.5;
$normval["6.02"]=0.5;
$normval["6.03"]=0.5;
$normval["6.04"]=0.5;
$normval["6.05"]=0.5;
$normval["6.06"]=0.5;
$normval["6.07"]=0.5;
$normval["6.08"]=0.5;
$normval["6.09"]=0.5;
$normval["6.10"]=0.5;
$normval["6.11"]=0.5;
$normval["6.12"]=0.5;
$normval["6.13"]=0.5;
$normval["6.14"]=0.5;
$normval["6.15"]=0.5;
$normval["6.16"]=0.5;
$normval["6.17"]=0.5;
$normval["6.18"]=0.5;
$normval["6.19"]=0.5;
$normval["6.20"]=0.5;
$normval["6.21"]=0.5;
$normval["6.22"]=0.5;
$normval["6.23"]=0.5;
$normval["6.24"]=0.5;
$normval["6.25"]=0.5;
$normval["6.26"]=0.5;
$normval["6.27"]=0.5;
$normval["6.28"]=0.5;
$normval["6.29"]=0.5;
$normval["6.30"]=0.5;
$normval["6.31"]=0.5;
$normval["6.32"]=0.5;
$normval["6.33"]=0.5;
$normval["6.34"]=0.5;
$normval["6.35"]=0.5;
$normval["6.36"]=0.5;
$normval["6.37"]=0.5;
$normval["6.38"]=0.5;
$normval["6.39"]=0.5;
$normval["6.40"]=0.5;
$normval["6.41"]=0.5;
$normval["6.42"]=0.5;
$normval["6.43"]=0.5;
$normval["6.44"]=0.5;
$normval["6.45"]=0.5;
$normval["6.46"]=0.5;
$normval["6.47"]=0.5;
$normval["6.48"]=0.5;
$normval["6.49"]=0.5;
$normval["6.50"]=0.5;
$normval["6.51"]=0.5;
$normval["6.52"]=0.5;
$normval["6.53"]=0.5;
$normval["6.54"]=0.5;
$normval["6.55"]=0.5;
$normval["6.56"]=0.5;
$normval["6.57"]=0.5;
$normval["6.58"]=0.5;
$normval["6.59"]=0.5;
$normval["6.60"]=0.5;
$normval["6.61"]=0.5;
$normval["6.62"]=0.5;
$normval["6.63"]=0.5;
$normval["6.64"]=0.5;
$normval["6.65"]=0.5;
$normval["6.66"]=0.5;
$normval["6.67"]=0.5;
$normval["6.68"]=0.5;
$normval["6.69"]=0.5;
$normval["6.70"]=0.5;
$normval["6.71"]=0.5;
$normval["6.72"]=0.5;
$normval["6.73"]=0.5;
$normval["6.74"]=0.5;
$normval["6.75"]=0.5;
$normval["6.76"]=0.5;
$normval["6.77"]=0.5;
$normval["6.78"]=0.5;
$normval["6.79"]=0.5;
$normval["6.80"]=0.5;
$normval["6.81"]=0.5;
$normval["6.82"]=0.5;
$normval["6.83"]=0.5;
$normval["6.84"]=0.5;
$normval["6.85"]=0.5;
$normval["6.86"]=0.5;
$normval["6.87"]=0.5;
$normval["6.88"]=0.5;
$normval["6.89"]=0.5;
$normval["6.90"]=0.5;
$normval["6.91"]=0.5;
$normval["6.92"]=0.5;
$normval["6.93"]=0.5;
$normval["6.94"]=0.5;
$normval["6.95"]=0.5;
$normval["6.96"]=0.5;
$normval["6.97"]=0.5;
$normval["6.98"]=0.5;
$normval["6.99"]=0.5;
$normval["7.00"]=0.5;
?>Calculate the probability you entered from the z-table of p(0 < z < 2.16)
For probability statements in the form P(a < z < b), this is calculated by finding P(b) - P(a)
P(z < 2.16) - P(z < 0.00)
From our z-table below, we find our two probabilities
p(0 < z < 2.16) = 0.5 -
p(0 < z < 2.16) =
0.5Z-table scores are below:
?>
| 0 | 0.01 | 0.02 | 0.03 | 0.04 | 0.05 | 0.06 | 0.07 | 0.08 | 0.09 |
0 | 0 | 0.004 | 0.008 | 0.012 | 0.016 | 0.0199 | 0.0239 | 0.0279 | 0.0319 | 0.0359 |
0.1 | 0.0398 | 0.0438 | 0.0478 | 0.0517 | 0.0557 | 0.0596 | 0.0636 | 0.0675 | 0.0714 | 0.0753 |
0.2 | 0.0793 | 0.0832 | 0.0871 | 0.091 | 0.0948 | 0.0987 | 0.1026 | 0.1064 | 0.1103 | 0.1141 |
0.3 | 0.1179 | 0.1217 | 0.1255 | 0.1293 | 0.1331 | 0.1368 | 0.1406 | 0.1443 | 0.148 | 0.1517 |
0.4 | 0.1554 | 0.1591 | 0.1628 | 0.1664 | 0.17 | 0.1736 | 0.1772 | 0.1808 | 0.1844 | 0.1879 |
0.5 | 0.1915 | 0.195 | 0.1985 | 0.2019 | 0.2054 | 0.2088 | 0.2123 | 0.2157 | 0.219 | 0.2224 |
0.6 | 0.2257 | 0.2291 | 0.2324 | 0.2357 | 0.2389 | 0.2422 | 0.2454 | 0.2486 | 0.2517 | 0.2549 |
0.7 | 0.258 | 0.2611 | 0.2642 | 0.2673 | 0.2704 | 0.2734 | 0.2764 | 0.2794 | 0.2823 | 0.2852 |
0.8 | 0.2881 | 0.291 | 0.2939 | 0.2967 | 0.2995 | 0.3023 | 0.3051 | 0.3078 | 0.3106 | 0.3133 |
0.9 | 0.3159 | 0.3186 | 0.3212 | 0.3238 | 0.3264 | 0.3289 | 0.3315 | 0.334 | 0.3365 | 0.3389 |
1 | 0.3413 | 0.3438 | 0.3461 | 0.3485 | 0.3508 | 0.3531 | 0.3554 | 0.3577 | 0.3599 | 0.3621 |
1.1 | 0.3643 | 0.3665 | 0.3686 | 0.3708 | 0.3729 | 0.3749 | 0.377 | 0.379 | 0.381 | 0.383 |
1.2 | 0.3849 | 0.3869 | 0.3888 | 0.3907 | 0.3925 | 0.3944 | 0.3962 | 0.398 | 0.3997 | 0.4015 |
1.3 | 0.4032 | 0.4049 | 0.4066 | 0.4082 | 0.4099 | 0.4115 | 0.4131 | 0.4147 | 0.4162 | 0.4177 |
1.4 | 0.4192 | 0.4207 | 0.4222 | 0.4236 | 0.4251 | 0.4265 | 0.4279 | 0.4292 | 0.4306 | 0.4319 |
1.5 | 0.4332 | 0.4345 | 0.4357 | 0.437 | 0.4382 | 0.4394 | 0.4406 | 0.4418 | 0.4429 | 0.4441 |
1.6 | 0.4452 | 0.4463 | 0.4474 | 0.4484 | 0.4495 | 0.4505 | 0.4515 | 0.4525 | 0.4535 | 0.4545 |
1.7 | 0.4554 | 0.4564 | 0.4573 | 0.4582 | 0.4591 | 0.4599 | 0.4608 | 0.4616 | 0.4625 | 0.4633 |
1.8 | 0.4641 | 0.4649 | 0.4656 | 0.4664 | 0.4671 | 0.4678 | 0.4686 | 0.4693 | 0.4699 | 0.4706 |
1.9 | 0.4713 | 0.4719 | 0.4726 | 0.4732 | 0.4738 | 0.4744 | 0.475 | 0.4756 | 0.4761 | 0.4767 |
2 | 0.4772 | 0.4778 | 0.4783 | 0.4788 | 0.4793 | 0.4798 | 0.4803 | 0.4808 | 0.4812 | 0.4817 |
2.1 | 0.4821 | 0.4826 | 0.483 | 0.4834 | 0.4838 | 0.4842 | 0.4846 | 0.485 | 0.4854 | 0.4857 |
2.2 | 0.4861 | 0.4864 | 0.4868 | 0.4871 | 0.4875 | 0.4878 | 0.4881 | 0.4884 | 0.4887 | 0.489 |
2.3 | 0.4893 | 0.4896 | 0.4898 | 0.4901 | 0.4904 | 0.4906 | 0.4909 | 0.4911 | 0.4913 | 0.4916 |
2.4 | 0.4918 | 0.492 | 0.4922 | 0.4925 | 0.4927 | 0.4929 | 0.4931 | 0.4932 | 0.4934 | 0.4936 |
2.5 | 0.4938 | 0.494 | 0.4941 | 0.4943 | 0.4945 | 0.4946 | 0.4948 | 0.4949 | 0.4951 | 0.4952 |
2.6 | 0.4953 | 0.4955 | 0.4956 | 0.4957 | 0.4959 | 0.496 | 0.4961 | 0.4962 | 0.4963 | 0.4964 |
2.7 | 0.4965 | 0.4966 | 0.4967 | 0.4968 | 0.4969 | 0.497 | 0.4971 | 0.4972 | 0.4973 | 0.4974 |
2.8 | 0.4974 | 0.4975 | 0.4976 | 0.4977 | 0.4977 | 0.4978 | 0.4979 | 0.4979 | 0.498 | 0.4981 |
2.9 | 0.4981 | 0.4982 | 0.4982 | 0.4983 | 0.4984 | 0.4984 | 0.4985 | 0.4985 | 0.4986 | 0.4986 |
3 | 0.4987 | 0.4987 | 0.4987 | 0.4988 | 0.4988 | 0.4989 | 0.4989 | 0.4989 | 0.499 | 0.499 |
How does the Z Score Lookup Calculator work?
Free Z Score Lookup Calculator - Given a Z-score probability statement from the list below, this will determine the probability using the normal distribution z-table.
* P(z < a)
* P(z <= a)
* P(z > a)
* P(z >= a)
* P(a < z < b)
Calculates z score probability
This calculator has 1 input.
What 1 formula is used for the Z Score Lookup Calculator?
What 4 concepts are covered in the Z Score Lookup Calculator?
- distribution
- value range for a variable
- probability
- the likelihood of an event happening. This value is always between 0 and 1.
P(Event Happening) = Number of Ways the Even Can Happen / Total Number of Outcomes - z score
- the number of standard deviations from the mean a data point is. Also known as a standard score
- z score lookup
Example calculations for the Z Score Lookup Calculator
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