ࡱ>  , Worksheet&Tools&WindowChart&Tools&WindowVisual Basic Module&Tools&Window\pharris_d B=j(9jJ2BBB S Empirical vs. Theoretical ,  9Qit[x  MbP?_*+%,&APage &PM \\JUPITER\maths1_34_hp-2300-0C odXXLettern0 4 DINU"4$IUPHdLetter [none] [none]Arial< 4P d?HARRIS_D<Automatic>0    <j i k k m m "dXX??:# RANDBETWEENU} DB} DB} DB} $DB} "DB}  "DB}  DB} IDB} $#DB} #DB} m#DB}  DB  X @ @ k@ ?@ ?@ ?@ ?@ ?@ ?@ ?@ ?@ ?@ ?@ ?@ ?@ ?@ ?@ ?@ ?@ ?@ ?@ ?@ ?@ ?@ ?@ ?@ ?@ ?@ ?@ ?@ ?@:,2Compare Experimental and Theoretical Probabilities  !   ! Results Sum*Experimental Frequency0Expeceted Frequency $ %Die1  &Die2  &Sum~ @#+@d F %g 2AZ$9'@ #901OB9 (@ #901OB (@  # LL~ @#+@ %g 3AZ$9'@ #901OB9 (@ #901OB ( @  ~ @#+@ %g 4AZ$9'@ #901OB9 (@ #901OB (@  ~ @#+*@ %g 5AZ$9'@ #901OB9 (@ #901OB (@  ~ @#+1@ %g 6AZ$9'@ #901OB9 (? #901OB (@  ~ @# +2@ %g 7AZ $9 '@ #901OB9 (@ #901OB ($@  ~  @# +,@  %g 8AZ $9 '@ #901OB9 (@ #901OB ($@  ~ "@# +&@  %g 9AZ $9 '@ #901OB9 (@ #901OB (@  ~ $@$ +"@ %g 10AZ $9 '@ #901OB9 (@ #901OB ($@  ~ &@$ +@ %g 11AZ $9 '@ #901OB9 (@ #901OB (@  ~ (@$+? %g 12AZ$9'? #901OB9 (@ #901OB (@  - Created by:../))9'@ #901OB9 (@ #901OB (@  -Hollylynne Stohl Drier../))9'@ #901OB9 (? #901OB (@  1-)Center for Technology & Teacher Education../))9'@ #901OB9 (? #901OB (@  -University of Virginia../))9'@ #901OB9 (@ #901OB ( @  .../))9'@ #901OB9 (@ #901OB ( @  $))9'@ #901OB9 (@ #901OB (@  $))9'@ #901OB9 (@ #901OB ("@  $))9'? #901OB9 (@ #901OB (@  $))9'@ #901OB9 (@ #901OB ( @  $))9'@ #901OB9 (@ #901OB ((@  $))9'@ #901OB9 (@ #901OB ( @  $))9'@ #901OB9 (@ #901OB (@  $))9'@ #901OB9 (@ #901OB ($@  $))9'? #901OB9 (@ #901OB (@  $))9'@ #901OB9 (@ #901OB (@  $))9'@ #901OB9 (@ #901OB (@  $))9'@ #901OB9 (@ #901OB (@  DGlb!  ?@! ?@" ?@# ?@$ ?@% ?@& ?@' ?@( ?@) ?@* ?@+ ?@, ?@- ?@. ?@/ ?@0 ?@1 ?@2 ?@3 ?@4 ?@5 ?@6 ?@7 ?@8 ?@9 ?@: ?@; ?@< ?@= ?@> ?@? ?@ $))9 '@ #901OB9 (@ #901OB ("@ ! !$))9!'@! #901OB9! (@! #901OB! (@ " "$))9"'@" #901OB9" (@" #901OB" ($@ # #$))9#'@# #901OB9# (@# #901OB# ("@ $ $$))9$'@$ #901OB9$ (@$ #901OB$ ("@ %$ $C LL %$))9%'@% #901OB9% (@% #901OB% (@ &$ &$))9&'@& #901OB9& (@& #901OB& (@ '$ '$))9''@' #901OB9' (?' #901OB' (@ ($ ($))9('?( #901OB9( (?( #901OB( (@ )$ )$))9)'@) #901OB9) (@) #901OB) (&@ *$ *$))9*'@* #901OB9* (@* #901OB* (@ +$ +$))9+'@+ #901OB9+ (@+ #901OB+ (@ ,$ ,$))9,'@, #901OB9, (?, #901OB, (@ -$ -$))9-'@- #901OB9- (@- #901OB- ($@ .$ .$))9.'@. #901OB9. (?. #901OB. (@ /$ /$))9/'?/ #901OB9/ (?/ #901OB/ (@ 0$ 0$))90'@0 #901OB90 (@0 #901OB0 (@ 1$ 1$))91'@1 #901OB91 (?1 #901OB1 (@ 2$ 2$))92'@2 #901OB92 (@2 #901OB2 (@ 3$ 3$))93'@3 #901OB93 (@3 #901OB3 (@ 4$ 4$))94'@4 #901OB94 (@4 #901OB4 ($@ 5$ 5$))95'?5 #901OB95 (?5 #901OB5 (@ 6$ 6$))96'?6 #901OB96 (@6 #901OB6 (@ 7$ 7$))97'@7 #901OB97 (@7 #901OB7 (@ 8$ 8$))98'@8 #901OB98 (?8 #901OB8 (@ 9$ 9$))99'@9 #901OB99 (@9 #901OB9 ("@ :$ :$))9:'@: #901OB9: (@: #901OB: ($@ ;$ ;$))9;'?; #901OB9; (@; #901OB; (@ <$ <$))9<'@< #901OB9< (@< #901OB< ( @ =$ =$))9='@= #901OB9= (@= #901OB= (@ >$ >$))9>'@> #901OB9> (@> #901OB> (@ ?$ ?$))9?'?? #901OB9? (?? #901OB? (@ @$ Dl@ ?@A ?@B ?@C ?@D ?@E ?@F ?@G ?@H ?@I ?@J ?@K ?@L ?@M ?@N ?@O ?@P ?@Q ?@R ?@S ?@T ?@U ?@V ?@W ?@X ?@Y ?@Z ?@[ ?@\ ?@] ?@^ ?@_ ?@ @$))9@'?@ #901OB9@ (@@ #901OB@ (@ A$ A$))9A'@A #901OB9A (?A #901OBA (@ B$ B$))9B'@B #901OB9B (@B #901OBB ( @ C$ C$))9C'@C #901OB9C (@C #901OBC (&@ D$ D$))9D'@D #901OB9D (@D #901OBD (@ ED Dg $ LL E$))9E'@E #901OB9E (@E #901OBE (@ FD F$))9F'?F #901OB9F (@F #901OBF (@ GD G$))9G'@G #901OB9G (@G #901OBG (@ HD H$))9H'@H #901OB9H (@H #901OBH ( @ ID I$))9I'@I #901OB9I (@I #901OBI ("@ JD J$))9J'@J #901OB9J (@J #901OBJ ( @ KD K$))9K'?K #901OB9K (@K #901OBK (@ LD L$))9L'@L #901OB9L (@L #901OBL ("@ MD M$))9M'@M #901OB9M (@M #901OBM (@ ND N$))9N'?N #901OB9N (@N #901OBN (@ OD O$))9O'@O #901OB9O (@O #901OBO ("@ PD P$))9P'@P #901OB9P (@P #901OBP (@ QD Q$))9Q'?Q #901OB9Q (@Q #901OBQ (@ RD R$))9R'@R #901OB9R (?R #901OBR (@ SD S$))9S'@S #901OB9S (@S #901OBS ( @ TD T$))9T'@T #901OB9T (@T #901OBT (&@ UD U$))9U'?U #901OB9U (@U #901OBU (@ VD V$))9V'@V #901OB9V (@V #901OBV (@ WD W$))9W'?W #901OB9W (@W #901OBW (@ XD X$))9X'@X #901OB9X (@X #901OBX ("@ YD Y$))9Y'@Y #901OB9Y (@Y #901OBY ("@ ZD Z$))9Z'@Z #901OB9Z (@Z #901OBZ ("@ [D [$))9['@[ #901OB9[ (@[ #901OB[ ($@ \D \$))9\'?\ #901OB9\ (@\ #901OB\ (@ ]D ]$))9]'@] #901OB9] (@] #901OB] (@ ^D ^$))9^'?^ #901OB9^ (@^ #901OB^ (@ _D _$))9_'@_ #901OB9_ (@_ #901OB_ (@ `D Dl` ?@a ?@b ?@c ?@d ?@e ?@f ?@g ?@h ;i ;j ;k ;l ;m ;n ;o ;p ;q ;r ;s ;t ;u ;v ;w ;x ;y ;z ;{ ;| ;} ;~ ; ; `$))9`'@` #901OB9` (@` #901OB` (@ aD a$))9a'@a #901OB9a (@a #901OBa ( @ bD b$))9b'?b #901OB9b (@b #901OBb (@ cD c$))9c'@c #901OB9c (@c #901OBc ( @ dD d$))9d'?d #901OB9d (@d #901OBd (@ eD e$))9e'@e #901OB9e (@e #901OBe ( @ fD f$))9f'@f #901OB9f (@f #901OBf (@ gD g$))9g'@g #901OB9g (@g #901OBg ( @ D h$)) h i$)) i j$)) j k$)) k l$)) l m$)) m n$)) n o$)) o p$)) p q$)) q r$)) r s$)) s t$)) t u$)) u v$)) v w$)) w x$)) x y$)) y z$)) z {$)) { |$)) | }$)) } ~$)) ~ $))  D l  ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; $))  $))  $))  $))  $))  $))  $))  $))  $))  $))  $))  $))  $))  $))  $))  $))  $@, ]V$D# @OPtOText 3r(1) Use the theoretical probabilties of totals of 2,3,...12 to find the expected frequency for each sum occurring in 100 rolls and enter your answers in cells C5 - C15 using either exact values or formulae. (2)In a word document, explain how you worked out the expected frequency. (3)Then copy and paste one trial in which the experimental frequency comes very close to the expected frequency and another for which they are far apart.K$Q?ZMUY|;I]> @nO4[MO  ,&APage &P"Pag??3@7!323   4  3Q: Experimental FrequencyQ;Q;3      4E4  3Q: Expeceted FrequencyQ;Q;3      4E4D FA 5 3OA3 & 43*D@@N#& ! 4%3O&Q Sums'4%e3O+&Q  Frequency'4523  43" 3Oq!%3O&Q423  44$%3O&Q4444  @ @ &@ @0@(@4@$@&@@@ ]F  X Picture 7  qq–yz}ddhQQUCCG559))-""&!%))/339??DMNP^_astvݼ~~`aeHHM99=-.2%%*$       "##(*+/55:CDHXX]stx~}[[^>=A""&  337PPTqquݺMMQ""& ==Aqqv矠\]_))-   #PPSϛddg::>   217TTX<զrqt>=A  /.4a_d}|~337   "#'efgԋ=<@ 666稦bae..3 .-.ΔJIM  '&'wwz%%*  jeb<񭬮LLP  (*NP@~ݘ@@C  ''EC=mhdTPN955-**<9;}ؒ?>C  /./"!#   +).wvz芉65:656oomIIG !!&jim灀..1   545>>< #[Z\ً..2 9::_\Z "kjlޓ77< <))*~|=:8 "!&vvy򚚝AAE qpnօx$#!)(-zy{󴳵DDG DLKᶻ%2)  ./.POS) < @ @ @ +  & @ A ? B \&(αLA ? AA @ @ @ @ @) & @ @ @ A A 2   + A A A@ @ A ? ' 1 AAB EHGFL*-]SRxx{  gm# - m%0߲OYh" % `|5 * r6>ob`iqmwZY'1   FO옘$$)  !%$ #6 [ % $#-nxӍ!5! " " " ! ! ! " $4 8  $$ " " $QO $ # ! !!"#fp¾筮FW " ! "##M]SSW  !"< !0  $ " ,vdf "  !"! #3 6  !   ! #Q _" # ##"![j?Q"!""!>Ollo!  ""0 "$"!.yMO#" ""!"## #$4 7  !!!"# Z )/<@KQCL$n"NZ5C! 2@66: !#!4 4  " ##".vtoy;<$# "##!x' 8  """"#[+1^e+/'8:  %.4215#BR4K  '04 '3J|yIIM #"!<a " """-ktnXSi*+$""# #PST5 8 $! ! ##aDI)>B3FA 7.e1p1n4p:zJEkKKNPwr:fɖBBG #"!f "!!!)GO;#$P #"!! #S7 #!!"#:pt#+47,4&;DcaqE*h_yW%aUn]Oi6./Os܃ ! # "!!"!"!< %+50N""!" #S7  #"!" #h66JHXS`]TO5=D`ZlG8~?LH`dC/ldwHHM[G"N;yk~NMQ!"! !! ""! "!" ! & N #!"" #X  6  $"!! "P <22rpd_kG9=B;@gm}svuy  "!!!""""!"$ N #!!" #s3 9 % 6  ! " "" "PF "74nVetF;FU8?&YdvFCRe`/t &@b^z`JJM  "!!  !!""!!"$ M ! "!! " 7 6  !#""$OQ 43g_KG]H>NeFGD/e*`buECSit7|$*>T@pap|{~''* " "!!!!!"" !" # M ! "!!!"""$G 6  ##"" $O c48vtYER>5tOx]kf<2qdzV'^YnڒC15>M.oifh::>  " !!  !"""!" # M"!!!!"" # $I 6 $#" " #O " z (&`cbHFk*b!T@tgn\+c6|hj6xUd̫E8;7~B#SY_Ze墡 " " !! %& %!# !# N" "!!<##$% &L 6  $ " " ! !O (  -S0|&m ]+e-">/v=6 W*fgd)^.p5~&^$$}HT:)k2x3v=wmlo " "" #8+?3 # !# N#"!!#g- 6 $"!! #O ; "# $ $!*33+*$ +"!$')0&7&5'1=Z_6t?JxdOy2w  ''/%05KS~<;>  " !!! AQIX)= #!$ N#"!" $u6 8 '7 #"!" $N _O"[&4%4#n"zv`6!J$r$pdl_7e&DnM%8+o\ޡx`]UhiE"Fgv3p`vϿ   !"!! cnfp.B " % M#" " " $P8  #!!" %N +- u{(ԧ'j$k%)&%%ڋ'G$ك')(έ%&#gך3#181"ϼ&ڄ%r$ϳ%)ݍ17ȏtrw ! !""!!&,> "$ M# ! !# $T 6  #   ! "MPX$;%؏$ٍ$'!)܅&ؑ&д''؇%֯'%{~#Ժ'a$!Y Ϋ!#vy &ѧ']'ԡ((Ҟ%YլgVVZ!" ! #,@飯)< # # M# ""$ $S9  # "#P N9ë$&ו%ۃ%(%z|rp${%v%ԙ')Ԗ&Ԭ'& ik!(ۊ&!>!ُ$'x{%)b%֎&λ(ʹ(\Kޠ9:>( 4! !!%Tg&8#M \ _ P ; 9_ \<  # \ ] @ / X% ς$֛%{%ҩ&&$ׇ%e$h%ҟ'ԙ&Ҳ'($fh'Ԯ&3"*"l%(!(w%ڀ&Ԫ((p2Â|~!& 1h!"^ -   $ )&" *(!7&;( ( * *!$M " - & & ) * % $ %& , - ) $" " & * - ( & % "Yi\0*ԥ'|%؇$'%#$ϧ%l%I$f#ה%ҭ'('ut%'e$3"V$ͻ'!~'ؕ'x&ږ''!w"ibbh R.+>;.)vS?JbQ 4ntR C_^$NskB%`r>o뷆t+Ossomu$ +K 3c!}TSh"TTj< ,I"$xN 3[ytispH!r 9veHͲBͳ*؊&g'(% %؞(p'{%׎&؇&ם&'}$)д(u&h%՛&%y'Ѵ(w&ށ&)®(p$ъ^LLQ Q,*:9/,.*,)&$K$#/-(& &Q('/---*)" 3! -,0+7$22%V(>l_iz%x241/5/rNs,:$"-<$"-8s,314.W.3#)53n_%3;ԓf͹5ԡ"T%֘'Ÿ'%"'ت'u&f&Ԯ'֦'٫''"t!)(Ѻ(ڞ(ߌ'&"!'(&u&д')Ճ%Rݡ=4#N"1A(%2C'&3?"&2.-89}(54j*:9{#3˞7)q~̴Eе#`#V} "%υ$M"3"~$ɘ$ç#$OTΪ'Ų&ǧ&Ό%q$¡$  #q#W$ޅ%Ͻ'ކ%|I226Q,);9'%&%-,0/c*(43++# 1"!87/-)&0-73i$$FHffMA6͞3/n2pݭRO] }97߫+&{<2$D"->$!.¨?$$1ë< vs'$(5У6է|'2֦-Ī<#4ة4֯u'6֊3٭JvH%ǁ"m#N4Ya~|pC/^yrtCJK n%^gZLE[kb\a[^nrB/S ҡ%ۋ%xBtjmp().O,);7*$&%++/-a+(41** .!!77/,)'0-51j%#a`ɕPL{B2@-:) @P;Ѩyw>=&,rF4E2;'5"F8'#':)K81/<+M:4 3 ?,J7&[ /P;*H6H8:+ <-?,>,4.>-<A/,i0$=2>0*f.5y%"!3-       - i4%ά':`]VXZ !&O+*;8)$'%.+3-c((33.-=;! 76.,)&0,52i0.~}ȧa_@<*& 6%"jSQsrSL:7$$p6452*'%#<8%## /)=8"},+?:# ".+86ho,)75.-! K LM|}~|~88;;9D@=:g%#3121eD><;]]0SU   OM[Y[V(XNHDEHO,*;9'%(&/,2.e((4341%!k%#640-)'/-31hFCәjk.-M##0065;675%%q3432((#$:8$#" ,*:8 }*+<:! ++76v$$32./##{ m<=T{ǂ|tqv-0h$&//21t''})(S  %(588338P-*;9)),*0/./b*(649583&#'%314/-+/..- [da~ݤ20[.,-+# 3233$#l6563.+*(=9%""-*;8 !}-*=:# ".+:6|''54)*$!(%HF{[c⑰}MOd''.,63(#20('g&%-&%-S,,;;446444*.Y.)958592" .,958622&& 9vՀa_ǣwt"! 3&%5395<90/uY63948282@9' $0,<8!!~+*;:! ! -,88q%!727620>a#"32tuO[|yz^'H {$"#J    & 3 & * ) $ - ' 4 7 &KK9oukxxe((3 + : 4O6142"! 7 2?! .)bo,)>;11%%p ,(E 85BBV~h!" +< .<  |ZԏIH+  <($'$W  6u)$WU$!}BBFF{00gs'"?"%sse÷ᆩ|(("       $'ں{V%#     HKGIKA&&& vykʿұ*)'  ((ƨ/-     qta9:3  ό{    {vYßhfI    01+}44. ƽ`]O  &   40!WvxN--  DF?33.  ݲ4/'   ,,0    ZZS32-}|p̿̕   < !"&99= *+'llb/-- //,љ+,0KKO" 8:3u-++=>7ץ #  78<_`c%%*  FF?%%#RTGĹ٫%&   EFJuvx,,/  NLGRTH#$xҟ %UVZ67: \[U|##  =?2̿}}n%(,cfhAAE..+gg_qpf  TVDӺ粯VVI<-03w{|QRU  TULii_IHC  giU̾|p.,% 8;>jkm  tviZZS  '(!vwgtq\+) GKM)*/   OPJoocAA:  dcYݦn99'    `beDEI   ##!tXWP&$#  ]\QٜU')  !#'|abe         JJE==9 &' onaԨR#%      +,1                          feaּn bdg``c                         ^]W|ˬڻo#$  >>B镕!!&                          eb\ĽxqkZUQJEAB=4d_MͫǮ6:   rsv\\_                        zwq{mf^OIC4.,  NM<ӶԿOU$  128魬!!%                          $$%ֶlf_3-*   RSAԾ̬mt<   }}edg $<                        887fdZ&%"   ^\QѲ~K  ;;>JHM                       UUQƽNP@  22*uֽ[  0/4.-2                        '('wvqEH4 CD7ǝq''dbfllo                    <=;ٹ77&   @@2з35"  JIM337                      PPLԧ     530˖CG(   $$(ى&&*                   fe`̕     /.(rʌDF%  wxzllo&'*     <            zytξo     ++vu\ɆEE%JLN^]`                   ++(ƮqtT    ')giFӹύKL+     @AD]^a                    EEAprH    (+fjEбԎTV-   >?B뫭RTW                    \\VڣEG+  ^a:֣ߵtcg%    56:窫BEG               lldӐz-/     TV.ՑߨߚׂLZ\   //2񪪬CEH             ttlƾИx99    JK$|ܟߪzO/,    .02񪪬RTV          <   yՒ-0    HM^ڑߜzVz{0  89=檬\^a          ΄u   36uy*f}{iDed+77  BCG뷸__b&(+       ;nlb      +, vy7LJ^^473     EEHkmp$'*       蹹VWO    ((11!"     RSVԈ368     kld   '*-y{~ڨhjl-/3 Ԑ//(  #TVXʃHIM# <ߩII> 79=lnqddh #  {ᰯRSG     LMQީ]^`#$&sohúߦCE;  DFJǗdce=44RNFޠ<>5 #MNQÛ]YX002  *(#xޜ892&),IKNvwžMMS"'  NMHڕ12,   <=@{{~ݲNMP#"& )(${votsj<  =?Amnpվa`bUSSlieEE> "#':;@VW[tux\]X456*+,###         "'(*/138=>BLNQbeg˭rtt___JJI787),. #%"%(+369DFIWX\lnr=   " Oh+'0PHPx Educational Technology Centerr harris_dal @ŏs@^{@qH(G75# `&" WMFC elT75# EMF"    !" !" !  " !  U'%    &% 6[% LdTZ!??% 969% Ld999!??% V6V% LdVVV!??% t6t% Ldttt!??% 6% Ld!??% 6% Ld!??% 6% Ld!??% 6% Ld!??% 6% Ld!??% 6% Ld!??% 6% Ld!??% 060% Ld000!??% E6E% LdEEE!??% Z6Z% LdZ!??% 6% Ld!??% W6W% LdWWW!??% 6% Ld!??% S6S% LdSSS!??% [6[% Ld[[[!??% 6% Ld!??% 6% Ld!??% 6% Ld!??'%  Ld!??'%  ( &% 6% Ld!??% 6% Ld!??%  ( &% 6% Ld!??% 6% Ld!??% % Rp"Geneva  C ~C ~ ~: ~: ~ q20,M ()T0MX`"GenevaHZ ~N ~ \XM<$0 dv%    TT %4AUuA %LP1   ( &% 6% Ld!??   TT BQAUuA BLP2   % :6:% Ld:::!??   TT `oAUuA `LP3   % W6W% LdWWW!??   TT AUuA LP4   % u6u% Lduuu!??   TT AUuA LP5   % 6% Ld!??   TT AUuA LP6   % 6% Ld!??   TT AUuA LP7   % 6% Ld!??   TT AUuA LP8   % 6% Ld!??   TT AUuA LP9   % 6% Ld!??   TX AUuA LP10   % &" WMFC E6% Ld!??   TX.AUuALP11   % 6% Ld!??   TX4CAUuA4LP12   % 161% Ld111!??   TXITAUuAILP13   % F6F% LdFFF!??   TT5=AUuA5LPA    % 6% Ld!??   TTAUuALPB    % X6X% LdXXX!??   TTAUuALPC    % 6% Ld!??   TTUZAUuAULU[PD    % T6T% LdTTT!??   TTltAUuAlLPE    % \6\% Ld\\\!??   TTAUuALPF   % 6% Ld!??   TTAUuALPG    % 6% Ld!??% % " !% %   U'%     Ldtd!??LdtWTt>!??'*o% (  *oLdWtTWt!??'% (  LdtSTtx!??'% (  LdStTSt]!??Rp Arial$V` ~Сq20L[)T0[4 [ Arial`[ C> ~N ~ \4[$0 dv%    Tx\8AUuA\2LCompare Experimental and Theoretical Probabilities           Rp"GenevaC ~C ~ ~: ~: ~ iq20l [)T0[4["Genevaoww[C> ~N ~ \4[$0 dv% Rp Bookman Old StyleX` ~Сq204 [)T0 [4$[Bookman Old Styleoww[C> ~N ~ \4 [$0 dv% % % " !% %   u%   T`&KAUuA&LTSum % % % " !% %   Xu% % %   TbuAUuAbu LhExperimental    TnAUuAn L`Frequency  % % % " !% %   uS% % %   TuFAUuAu L`Expeceted  TBAUuA L`Frequency  % Rp Bookman Old StyleX` ~Сq20)T0 4$(M Bookman Old Style8MC> ~N ~ \4 $0 dv% % % " !% %   U%   TT4>AUuA4LP2 TTAUuALP2 TT4>AUuA4LP3 TTAUuALP7 TT4>AUuA4LP4 TTAUuALP8 TT4>AUuA4LP5 TTAUuALP9 TT4>AUuA4LP6 T&" WMFC %XAUuALP16 TT4>AUuA4LP7 TXAUuALP14 TT4>/AUuA4LP8 TX/AUuALP19 TT42>DAUuA42LP9 TT2DAUuA2LP9 TX/GCTAUuA/GLP10 TTGTAUuAGLP8 % % " !% %   U' % (     ( &% % Ld!??% % LdW!??% % Ld!??% % LdS!??% % Ld[!??% % Ld!??% % Ld!??% % Ld!??'%   ( &% t6Tt% LdtStt9!??% 6T% LdS9!??% 6T% LdS9!??% 6T% LdS9!??% 6T% LdS9!??% 6T% LdS9!??% 6T% LdS9!??% 6T% LdS9!??% 06T0% Ld0S009!??% E6TE% LdESEE9!??% Z6TZ% LdZ9!??% t6\% LdtTt!??% Wu6W\% LdWuWTWu!??% u6\% LduTu!??% Su6S\% LdSuSTSu!??% ( % " !%   UU 0  % %   % % !&% ' % % % % " !% % %   % % % " !% % %   Rp "Geneva  C ~C ~ ~: ~: ~t mq20M )T0hM4M "Geneva8MC> ~N ~ \4hM$0 dv% Rp"Small Fonts\\dGOText 3ervicht0X\(tX4<?00Y0 X0\"Smll Fontsdv% Rp"Geneva  C ~C ~ ~: ~: ~D %q20M ()T0MXt"GenevaHZ ~N ~ \XM<$0 dv% % % % % % % % % % % % % % % % % % % % % % % % % % Rp"Small Fonts:R.tK&wl(*8R܌!pg0 X0́\"Smll Fonts dv% % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % " !% % %   ])&% ( '% (    +W$% % % " !% % %   ])' % ( % (    V0T6WW66&% % % % " !% % %   6WR=6   6W66W66W6&" WMFC 6W6g6Wg6K6WK6/6W/66W% % % " !% % %   ])R=&% ( 6  6W6W6666% % % " !% % %   ])% % % " !% % %   X$% % % " !% % %   6X% % % " !% % %   6Y&% ( '% (    V0;CC;;V0ATU]]UUV0;TpxxppV05TV0TV0TV0V0V0   V0'//''V0BJJBB% % % " !% % %   6X% % % " !% % %   ])& % ( 6  66% 1661661661661661g66g1K66K1/66/16666W666P6Pk6k666666"6"=6=W6W% % % " !% % %   ])% % % " !% % %   ])    TTAUuA LP0 TTsC{TAUuA LP5 TXj'{9AUuALP10 TXj {AUuALP15 TXj{AUuA{LP20 TXj{AUuA^LP25 TXj{AUuABLP30 TXj{AUuA&LP35 TXj~{AUuA LP40 % % % " !% % %   ])% % % " !% % %   ])  TTAUuA?LP2 TTAUuAYLP3 TTAUuAtLP4 TTAUuALP5 TTAUuALP6 TTAUuALP7 TTAUuALP8 TTAUuALP9 TXAUuA LP10 TXAUuA'LP11 TXAUuAALP12 % % % " !% % %   ])% % % % % % " !% % %    $  TdAUuALTSums  % % % % " !% % %   ])% % % % % " !% % %   `  Rp"Geneva ~ 8b ~ + C> ~N ~D &\x9w$0D &dv% T[iAUuA L`Frequency% ( % % % % " !% % %   ])% '% (     +Q=% % % " !% % %   Q<% % % " !% % %   Q<&% ( ' % (     +  TAUuALxExperimental Frequency % % % " !% % %   Q<% % % " !% % %   Q<&% ( '% (    +-4  TAUuA)LtExpeceted Frequency% % % " !% % %  &:WMFC Q<% % % " !% % %   ])% % % " !% % %   ])& % ( % (    +W$% % ( " !  ])" U!  " !  " % % K@0 UU  % " !  U' %    % 6% Ld!??% 6U% LdTU!??% "   U  '' ' ,U-  -[- @ !Z-99- @ !9-VV- @ !V-tt- @ !t-- @ !-- @ !-- @ !-- @ !-- @ !-- @ !-- @ !-00- @ !0-EE- @ !E-ZZ- @ !Z-- @ !-WW- @ !W-- @ !-SS- @ !S-[[- @ ![-- @ !-- @ !-- @ !-  @ !- -- @ !-- @ !- -- @ !-- @ !--"Geneva-  2 % 1 -- @ !  2 B 2 -::- @ !:  2 ` 3 -WW- @ !W  2 4 -uu- @ !u  2 5 -- @ !  2 6 -- @ !  2 7 -- @ !  2 8 -- @ !  2 9 -- @ !  2 10 -- @ !  2 11 -- @ !  2 412 -11- @ !1  2 I13 -FF- @ !F  2 5A  -- @ !  2 B  -XX- @ !X  2 C  -- @ !  2 UU[D  -TT- @ !T  2 lE  -\\- @ !\  2 F -- @ !  2 G  -- @ !-"System-'-- ,U-    @ !d @ !>t*o-   *o @ !tW-    @ !xt-    @ !]tS Arial-  R2 \2Compare Experimental and Theoretical Probabilities           "Geneva- Bookman Old Style- --'- -  ,u-   2 &Sum - --'- -  ,uX- - -  2 ub Experimental   2 n Frequencyt  - --'- -  ,Su- - -  2 u Expeceted  2 Frequency  - Bookman Old Style- --'- -  ,U-   2 42 2 2 2 43 2 7 2 44 2 8 2 45 2 9 2 46 2 16 2 47 2 14 2 48 2 19 2 249 2 29 2 G/10 2 G8 --'- -  ,U-   -- @ !-- @ !W-- @ !-- @ !S-- @ ![-- @ !-- @ !-- @ !-  -ttT- @ !9t-T- @ !9-T- @ !9-T- @ !9-T- @ !9-T- @ !9-T- @ !9-T- @ !9-00T- @ !90-EET- @ !9E-ZZT- @ !9Z-t\- @ !t-uW\W- @ !uW-u\- @ !u-uS\S- @ !uS- -'-  ,U,U - - -- -----'- -- ---'- -- "Geneva-"Small Fonts-"Geneva--------------------------"Small Fonts-- -- -- ------------------- - ---------'--- ,UtS--  yX---'--- ,UtS--  $hh----'--- ,U,UL L00---'--- ,UtS,UtS- hh---'--- ,UtS---'--- ,UyX---'--- ,U---'--- ,U--  $]]hh]$AAhhA$;;hh;$55hh5$hh$hh$,44h,h,$F5N5NhFhF5$`;h;hh`h`;$zLLhzhzL$WWhhW---'--- ,U---'--- ,UtS- h- hhLL00hhmcmcmcmcmcm c m'c'mAcAm[c[mucumcmc---'- -- ,UtS---'- -- ,UtS   2 _s0 2 Cs5 2 'j10 2 j15 2 j20 2 j25 2 j30 2 j35 2 ~j40 ---'- -- ,UtS---'- -- ,UtS  2 w2 2 w3 2 w4 2 w5 2 w6 2 w7 2 w08 2 wJ9 2 w_10 2 wz11 2 w12 ---'- -- ,UtS------'--- ,  2 Sums  ----'--- ,UtS-----'--- ,oX "Geneva-2 [ Frequency-----'--- ,UtS--  ---'--- ,---'--- ,--   (2 Experimental Frequency ---'--- ,---'--- ,--   $2 Expeceted Frequencyn---'--- ,---'--- ,UtS---'--- ,UtS--  yX--' ,UtS' ' '--,U -' ,U-  -- @ !-U- @ !U-'՜.+,00 8@ H n Empirical vs. Theoretical  Worksheets  !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~Root EntryFBook SummaryInformation(DocumentSummaryInformation8