{VERSION 4 0 "IBM INTEL NT" "4.0" } {USTYLETAB {CSTYLE "Maple Input" -1 0 "Courier" 0 1 255 0 0 1 0 1 0 0 1 0 0 0 0 1 }{PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }1 1 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "Headi ng 1" -1 3 1 {CSTYLE "" -1 -1 "Times" 1 18 0 0 0 1 2 1 2 2 2 2 1 1 1 1 }1 1 0 0 8 4 1 0 1 0 2 2 0 1 }{PSTYLE "Heading 2" -1 4 1 {CSTYLE "" -1 -1 "Times" 1 14 0 0 0 1 2 1 2 2 2 2 1 1 1 1 }1 1 0 0 8 2 1 0 1 0 2 2 0 1 }{PSTYLE "Warning" -1 7 1 {CSTYLE "" -1 -1 "Courier" 1 10 0 0 255 1 2 2 2 2 2 1 1 1 3 1 }1 1 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "Maple Plot" -1 13 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }3 1 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "Normal" -1 256 1 {CSTYLE " " -1 -1 "Times" 1 12 0 0 0 1 2 1 1 2 2 2 1 1 1 1 }1 1 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "Normal" -1 257 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 1 1 2 2 2 1 1 1 1 }1 1 0 0 0 0 1 0 1 0 2 2 0 1 }} {SECT 0 {PARA 4 "" 0 "" {TEXT -1 19 "Module 5: Statistcs" }}{PARA 0 " " 0 "" {TEXT -1 0 "" }}{PARA 3 "" 0 "" {TEXT -1 29 "502 : The Normal D istribution" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 " " }}{PARA 256 "" 0 "" {TEXT -1 17 "O B J E C T I V E" }}{PARA 0 "" 0 " " {TEXT -1 99 "In this project we will use the standard normal distrib ution and more general normal distributions." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 257 "" 0 "" {TEXT -1 9 "S E T U P" }}{PARA 0 "" 0 "" {TEXT -1 252 "In this project we will use the following command packag es. Type and execute this line before begining the project below. If y ou re-enter the worksheet for this project, be sure to re-execute this statement before jumping to any point in the worksheet." }}{PARA 0 " " 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "resta rt; with(plots):" }}{PARA 7 "" 1 "" {TEXT -1 50 "Warning, the name cha ngecoords has been redefined\n" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }} {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 83 "_______________________________________________ ____________________________________" }}{PARA 4 "" 0 "" {TEXT -1 44 "A . Z Scores Geometrically - Standard, Normal" }}{PARA 0 "" 0 "" {TEXT -1 83 "_______________________________________________________________ ____________________" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 " " {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 44 "Tables --> interactiv e numerical and graph" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 1078 "z_plot := proc(z) \nlocal x, xvalue, f, p, delta, index, n, area;\n\n f:= x -> exp( ( -x^2)/2)/sqrt(2*Pi) ;\n n := 120; delta := 8/n; index := 1; \n for xvalue from - 4 to 4 by delta do\n if( xvalue >= z) then \n p[index ] := plots[polygonplot]( [[xvalue, 0],[xvalue,f(xvalue)],[xvalue + del ta, \+ f(xvalue + delta)], [xvalue + delta, 0]],\n \+ color = red, style = patchnogrid );\n else \+ \n p[index] := plots[polygonplot]( [[xvalue,0 ],[xvalue,f(xva lue)],[xvalue + delta, f(xvalue + delta)], [xvalue + delta, 0]],color \+ = blue, style = patchnogrid ) ;\n fi; \n index := index + \+ 1;\n od;\n\narea := int( f(x), x = z..infinity);\nplots[display](s eq( p[i], i = 1..n-1),\ntextplot([-2,.1, cat(convert( evalf(100*(1 - a rea), 5), string),\"%\")],\n align = \{ABOVE, LEFT\} , font = [HEL VETICA, BOLD, 14]),\ntextplot([2,.1, cat(convert( evalf(100*(area), 5) , string),\"%\")],\n align = \{ABOVE, RIGHT\} , font = [HELVETICA, BOLD, 14])):\nend:" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 " " {TEXT -1 67 "To invoke this new polt command, simply type it and giv e a z-value." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "z_plot(1.234);" }} {PARA 13 "" 1 "" {GLPLOT2D 400 300 300 {PLOTDATA 2 "6er-%)POLYGONSG6%7 &7$$!\"%\"\"!$F*F*7$F($\"+dAIQ8!#87$$!+LLLLR!\"*$\"+#y:Mu\"F/7$F1F+-%' COLOURG6&%$RGBGF+F+$\"*++++\"!\")-%&STYLEG6#%,PATCHNOGRIDG-F$6%7&F6F07 $$!+nmmmQF3$\"+#Q)3hAF/7$FFF+F7F>-F$6%7&FJFE7$$!+++++QF3$\"+e#p%>HF/7$ FOF+F7F>-F$6%7&FSFN7$$!+LLLLPF3$\"+O-%Gv$F/7$FXF+F7F>-F$6%7&FfnFW7$$!+ nmmmOF3$\"+;lq-[F/7$F[oF+F7F>-F$6%7&F_oFjn7$$!+++++OF3$\"++$>!>hF/7$Fd oF+F7F>-F$6%7&FhoFco7$$!+LLLLNF3$\"+g5`hxF/7$F]pF+F7F>-F$6%7&FapF\\p7$ $!+nmmmMF3$\"+0'z7!)*F/7$FfpF+F7F>-F$6%7&FjpFep7$$!+++++MF3$\"+o\">AB \"!#77$F_qF+F7F>-F$6%7&FdqF^q7$$!+LLLLLF3$\"+&**yAa\"Fcq7$FiqF+F7F>-F$ 6%7&F]rFhq7$$!+nmmmKF3$\"+ozz@>Fcq7$FbrF+F7F>-F$6%7&FfrFar7$$!+++++KF3 $\"++#)3%Q#Fcq7$F[sF+F7F>-F$6%7&F_sFjr7$$!+LLLLJF3$\"+?rYWHFcq7$FdsF+F 7F>-F$6%7&FhsFcs7$$!+nmmmIF3$\"+GiV?OFcq7$F]tF+F7F>-F$6%7&FatF\\t7$$! \"$F*$\"+7%[=V%Fcq7$FftF+F7F>-F$6%7&FjtFet7$$!+LLLLHF3$\"+!=c5S&Fcq7$F _uF+F7F>-F$6%7&FcuF^u7$$!+nmmmGF3$\"+!4KIb'Fcq7$FhuF+F7F>-F$6%7&F\\vFg u7$$!+++++GF3$\"+!e^a\"zFcq7$FavF+F7F>-F$6%7&FevF`v7$$!+LLLLFF3$\"+Xws =&*Fcq7$FjvF+F7F>-F$6%7&F^wFiv7$$!+nmmmEF3$\"+-')fR6!#67$FcwF+F7F>-F$6 %7&FhwFbw7$$!+++++EF3$\"+ApHe8Fgw7$F]xF+F7F>-F$6%7&FaxF\\x7$$!+LLLLDF3 $\"+5ey6;Fgw7$FfxF+F7F>-F$6%7&FjxFex7$$!+nmmmCF3$\"+_**4/>Fgw7$F_yF+F7 F>-F$6%7&FcyF^y7$$!+++++CF3$\"+GIXRAFgw7$FhyF+F7F>-F$6%7&F\\zFgy7$$!+L LLLBF3$\"+4*)=AEFgw7$FazF+F7F>-F$6%7&FezF`z7$$!+nmmmAF3$\"+q4scIFgw7$F jzF+F7F>-F$6%7&F^[lFiz7$$!+++++AF3$\"+%Gfua$Fgw7$Fc[lF+F7F>-F$6%7&Fg[l Fb[l7$$!+LLLL@F3$\"+/cs)4%Fgw7$F\\\\lF+F7F>-F$6%7&F`\\lF[\\l7$$!+nmmm? 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"Curve 32" "Curve 33" "Curve 34" "Curve 35" "Curve 36 " "Curve 37" "Curve 38" "Curve 39" "Curve 40" "Curve 41" "Curve 42" "C urve 43" "Curve 44" "Curve 45" "Curve 46" "Curve 47" "Curve 48" "Curve 49" "Curve 50" "Curve 51" "Curve 52" "Curve 53" "Curve 54" "Curve 55 " "Curve 56" "Curve 57" "Curve 58" "Curve 59" "Curve 60" "Curve 61" "C urve 62" "Curve 63" "Curve 64" "Curve 65" "Curve 66" "Curve 67" "Curve 68" "Curve 69" "Curve 70" "Curve 71" "Curve 72" "Curve 73" "Curve 74 " "Curve 75" "Curve 76" "Curve 77" "Curve 78" "Curve 79" "Curve 80" "C urve 81" "Curve 82" "Curve 83" "Curve 84" "Curve 85" "Curve 86" "Curve 87" "Curve 88" "Curve 89" "Curve 90" "Curve 91" "Curve 92" "Curve 93 " "Curve 94" "Curve 95" "Curve 96" "Curve 97" "Curve 98" "Curve 99" "C urve 100" "Curve 101" "Curve 102" "Curve 103" "Curve 104" "Curve 105" "Curve 106" "Curve 107" "Curve 108" "Curve 109" "Curve 110" "Curve 111 " "Curve 112" "Curve 113" "Curve 114" "Curve 115" "Curve 116" "Curve 1 17" "Curve 118" "Curve 119" "Curve 120" "Curve 121" }}}}{PARA 0 "" 0 " " {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 476 "The horizontal axis is the z axis. The area is blue on the left of z = 1.234 and red on the \+ right of z = 1.234. The area of the red region represents the probabil ity that an arbitary value is greater than z = 1.234. The number on th e right side of the graph is the probability expressed iin a percentag e. The blue region and the number a+ left are the probability that an \+ arbitary value is less than z = 1.234. This is a lot more fun than loo king up values in a table isn't it" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }} {PARA 0 "" 0 "" {TEXT -1 36 "We can also enter negative z values." }} {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 116 "Nothe th at the red region is much larger now along with the probability associ ated with the red region P(z > -1.234)" }}{PARA 0 "" 0 "" {TEXT -1 0 " " }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "z_plot(-1.234);" }} {PARA 13 "" 1 "" {GLPLOT2D 400 300 300 {PLOTDATA 2 "6er-%)POLYGONSG6%7 &7$$!\"%\"\"!$F*F*7$F($\"+dAIQ8!#87$$!+LLLLR!\"*$\"+#y:Mu\"F/7$F1F+-%' COLOURG6&%$RGBGF+F+$\"*++++\"!\")-%&STYLEG6#%,PATCHNOGRIDG-F$6%7&F6F07 $$!+nmmmQF3$\"+#Q)3hAF/7$FFF+F7F>-F$6%7&FJFE7$$!+++++QF3$\"+e#p%>HF/7$ FOF+F7F>-F$6%7&FSFN7$$!+LLLLPF3$\"+O-%Gv$F/7$FXF+F7F>-F$6%7&FfnFW7$$!+ nmmmOF3$\"+;lq-[F/7$F[oF+F7F>-F$6%7&F_oFjn7$$!+++++OF3$\"++$>!>hF/7$Fd oF+F7F>-F$6%7&FhoFco7$$!+LLLLNF3$\"+g5`hxF/7$F]pF+F7F>-F$6%7&FapF\\p7$ $!+nmmmMF3$\"+0'z7!)*F/7$FfpF+F7F>-F$6%7&FjpFep7$$!+++++MF3$\"+o\">AB \"!#77$F_qF+F7F>-F$6%7&FdqF^q7$$!+LLLLLF3$\"+&**yAa\"Fcq7$FiqF+F7F>-F$ 6%7&F]rFhq7$$!+nmmmKF3$\"+ozz@>Fcq7$FbrF+F7F>-F$6%7&FfrFar7$$!+++++KF3 $\"++#)3%Q#Fcq7$F[sF+F7F>-F$6%7&F_sFjr7$$!+LLLLJF3$\"+?rYWHFcq7$FdsF+F 7F>-F$6%7&FhsFcs7$$!+nmmmIF3$\"+GiV?OFcq7$F]tF+F7F>-F$6%7&FatF\\t7$$! \"$F*$\"+7%[=V%Fcq7$FftF+F7F>-F$6%7&FjtFet7$$!+LLLLHF3$\"+!=c5S&Fcq7$F _uF+F7F>-F$6%7&FcuF^u7$$!+nmmmGF3$\"+!4KIb'Fcq7$FhuF+F7F>-F$6%7&F\\vFg u7$$!+++++GF3$\"+!e^a\"zFcq7$FavF+F7F>-F$6%7&FevF`v7$$!+LLLLFF3$\"+Xws =&*Fcq7$FjvF+F7F>-F$6%7&F^wFiv7$$!+nmmmEF3$\"+-')fR6!#67$FcwF+F7F>-F$6 %7&FhwFbw7$$!+++++EF3$\"+ApHe8Fgw7$F]xF+F7F>-F$6%7&FaxF\\x7$$!+LLLLDF3 $\"+5ey6;Fgw7$FfxF+F7F>-F$6%7&FjxFex7$$!+nmmmCF3$\"+_**4/>Fgw7$F_yF+F7 F>-F$6%7&FcyF^y7$$!+++++CF3$\"+GIXRAFgw7$FhyF+F7F>-F$6%7&F\\zFgy7$$!+L LLLBF3$\"+4*)=AEFgw7$FazF+F7F>-F$6%7&FezF`z7$$!+nmmmAF3$\"+q4scIFgw7$F jzF+F7F>-F$6%7&F^[lFiz7$$!+++++AF3$\"+%Gfua$Fgw7$Fc[lF+F7F>-F$6%7&Fg[l Fb[l7$$!+LLLL@F3$\"+/cs)4%Fgw7$F\\\\lF+F7F>-F$6%7&F`\\lF[\\l7$$!+nmmm? 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"Curve 19" "Curve 20" "Curve 21" "Curve 22" "Curve 23" "Curve 24" " Curve 25" "Curve 26" "Curve 27" "Curve 28" "Curve 29" "Curve 30" "Curv e 31" "Curve 32" "Curve 33" "Curve 34" "Curve 35" "Curve 36" "Curve 37 " "Curve 38" "Curve 39" "Curve 40" "Curve 41" "Curve 42" "Curve 43" "C urve 44" "Curve 45" "Curve 46" "Curve 47" "Curve 48" "Curve 49" "Curve 50" "Curve 51" "Curve 52" "Curve 53" "Curve 54" "Curve 55" "Curve 56 " "Curve 57" "Curve 58" "Curve 59" "Curve 60" "Curve 61" "Curve 62" "C urve 63" "Curve 64" "Curve 65" "Curve 66" "Curve 67" "Curve 68" "Curve 69" "Curve 70" "Curve 71" "Curve 72" "Curve 73" "Curve 74" "Curve 75 " "Curve 76" "Curve 77" "Curve 78" "Curve 79" "Curve 80" "Curve 81" "C urve 82" "Curve 83" "Curve 84" "Curve 85" "Curve 86" "Curve 87" "Curve 88" "Curve 89" "Curve 90" "Curve 91" "Curve 92" "Curve 93" "Curve 94 " "Curve 95" "Curve 96" "Curve 97" "Curve 98" "Curve 99" "Curve 100" " Curve 101" "Curve 102" "Curve 103" "Curve 104" "Curve 105" "Curve 106 " "Curve 107" "Curve 108" "Curve 109" "Curve 110" "Curve 111" "Curve 1 12" "Curve 113" "Curve 114" "Curve 115" "Curve 116" "Curve 117" "Curve 118" "Curve 119" "Curve 120" "Curve 121" }}}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 " " }}{PARA 0 "" 0 "" {TEXT -1 83 "_____________________________________ ______________________________________________" }}{PARA 4 "" 0 "" {TEXT -1 31 "B. General Normal, Distribution" }}{PARA 0 "" 0 "" {TEXT -1 83 "_______________________________________________________________ ____________________" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 " " {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 110 "The standard normal di stribution is a normal distribution where the mean is 0 and the standa rd deviation is 1." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 " > " 0 "" {MPLTEXT 1 0 1050 "x_plot := proc(x, mean, sd) \nlocal xvalue , f, p, delta, index, n, area;\n\n f:= u -> exp( ( -(u-2))/(sd*sqr t(2*Pi)));\n n := 120; delta := (8*sd)/n; index := 1; \n for xvalue from (mean - 4*sd) to (mean+4*sd) by delta do\n if( xv alue >= x) then \n p[index] := plots[polygonplot]( [[xv alue, 0],[xvalue,f(xvalue)],[xvalue + delta, f(xvalue + delta)], [xval ue + delta, 0]], color = yellow, style = patchnogrid );\n else \n p[index] := plots[polygonplot]( [[xvalue,0 ],[xval ue,f(xvalue)],[xvalue + delta, f(xvalue + delta)], [xvalue + delta, 0] ],color = green, style = patchnogrid ) ;\n fi; \nindex := in dex + 1;\nod;\n\narea := int( f(u), u = x..infinity);\nplots[display]( seq( p[i], i = 1..n-1),\ntextplot([-2*sd + mean,f(mean)/4, cat(convert ( evalf(100*(1 - area), 5), string),\"%\")],\n align = \{ABOVE, LE FT\} , font = [HELVETICA, BOLD, 14]),\ntextplot([2*sd + mean,f(mean)/4 , cat(convert( evalf(100*( area), 5), string),\"%\")],\n align = \+ \{ABOVE, RIGHT\} , font = [HELVETICA, BOLD, 14])):\n\nend:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 197 "To use this new command, we supply three param eters : a data value, the mean, and the standard deviation. For exampl e, if x = 13.2, the mean = 11.7, and the standard deviation is 2.3. 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