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  3llUb$V`ªztI*1    /9+s4@@  @ @ ?5               "  #          @ ?     currentQ         < @ ?/  +u title STATISTICS TOPIC 4 q1 Use Information A, below, to answer this question.  Which of the following statements about the values in the table of probabilities is not correct? q1a1 The probability of an employee taking 6 or more days of sick leave P(M) is 0.6 q1a2 The probability that an employee is on the Night Shift (N) and takes less than 6 days of leave (L), is called a conditional probability P(N | L) = 0.6 q1a3 If you know that an employee is on day shift (D) then the probability that they will take less than 6 days of leave (L) is the conditional probability  P( L | D) = 0.4 q1a4 The probability that an employee works Day Shift (D) or takes 6 or more days of leave (M) is found using the addition rule to be P( D or M) = 0.76 q1a5 They are all correct q1correct a2 q2 The analyst wishes to use the Probabilities table from Information A to determine whether the work shift variable and the number of days of sick leave variable are or are not independent variables. Which of the following statements about the work shift and the number of days of sick leave variables is correct ? q2a1 These variables are independent because the marginal probabilities such as P(L) are the same as the conditional probabilities P(L | D) q2a2 These variables are not independent because the marginal probability P(L) is different from the conditional probability P(N | L) q2a3 These variables are not independent because the joint probabilities such as P(L and N) are equal to the product of the probabilities P(L).P(N). q2a4 These variables are dependent because the marginal probabilities such as P(L) are equal to the conditional probability P(L | N) q2a5 None of the above q2correct a1 q3 Use the Information B below to answer this question.  If values are rounded to 3 decimal places which of the following is the correct pair of values for the mean, the variance or standard deviation of the number of arrivals at the counter. q3a1 Mean mu  =  2 and  variance sigma-squared =  1.265 q3a2 Mean mu  =  2.5 and  variance sigma-squared =  1.6 q3a3 Mean mu  =  2 and  standard deviation sigma =  1.6 q3a4 Mean mu  =  2.4 and  variance sigma-squared =  1.6 q3a5 q3correct a5 q4 Use the Information C below to answer this question. A total of n = 6 people are interviewed independently of each other. Which of the following statements about the probability that 5 out of the 6 complaints will be handled well is correct q4a1 less than 0.06 q4a2 between 0.23 and 0.24 q4a3 more than 0.35 q4a4 between 0.30 and 0.32 q4a5 q4correct a3 q5 Using Information C, which of the following statements about the probability that 4 or less of the 6 complaints will be handled well is correct q5a1 less than 0.36 q5a2 more than 0.52 q5a3 between 0.45 and 0.475 q5a4 between 0.15 and 0.175 q5a5 q5correct q6 Suppose the section manager from Information C is interested in the measures of central tendency and variation for the number of complaints which are handled well. Which of the following sets of values, where values are rounded to 3 decimal places, is the correct set of values q6a1 Mean mu  =  4.5  and  variance sigma-squared =  1.125 q6a2 Mean mu  =  4.5  and  variance sigma-squared =  1.061 q6a3 Mean mu  =  1.5  and  variance sigma-squared =  1.125 q6a4 Mean mu  =  1.5  and  standard deviation sigma =  1.061 q6a5 q6correct q7 Use Information D below to answer this question.  Which of the following statements concerning the probability that exactly 2 customers will arrive at the counter in a 5-minute period is correct q7a1 less than 0.05 q7a2 between 0.21 and 0.23 q7a3 between 0.16 and 0.18 q7a4 more than 0.25 q7a5 q7correct q8 Use Information D below to answer this question.  Which of the following statements concerning the probability that 3 or more customers will arrive at a counter in a 5-minute period is correct q8a1 between 0.10 and 0.15 q8a2 less than 0.23 q8a3 more than 0.77 q8a4 between 0.60 and 0.55 q8a5 q8correct a4 q9 The section manager from Information D is interested in the mean and variance of the number of customers who arrive during a 1 hour period. Which of the following is the correct set of values for these two measures q9a1 Mean mu  =  3  and  variance sigma-squared =  3 q9a2 Mean mu  =  36  and  standard deviation sigma =  1.732 q9a3 Mean mu  =  30 and  variance sigma-squared =  30 q9a4 Mean mu  =  36  and  standard deviation sigma =  6 q9a5 q9correct   < < < < 	< 
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&൤b7`#`$ttw)(o}02#/xpR0Q77`4LiH\'(v6)JLwM{{-n/أJ@˦;HD4݀ҩ b7`4NUch;Mkttw)(ƛU'I*׽4݀Jt`e@G@^`n0Q77`#`$ttw(b;HD4݀Jt`e,I*]14t
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&lR4݀Jt`e@G@^`n4݀Jt`e@G@^`n02#/xpR0Q77`#`$Lb;HD4݀Jt`ek4݀Jt`e@G@^`n_(vJƔLwM{{.Eo(v6)JLwM{{.D[x˦;HD4݀ҩ1 `.Hx˦;HD4݀ҩ:IT%i %X˦;HD$Uch;MM*I*]14t
F
&lR}02#/xpR0Q77`#`$b;HD4݀Jt`eZ4݀Jt`e@G@^`n4݀Jt`e@G@^`nI*]14t
F
&lR4݀Jt`e@G@^`nn02#/xpR0Q77`4LiH^02#/xpR0Q77`4LiH4݀ҩ:IV02#/xpR0Q7QnF%:IV02#/xpR0Q7nF%:IV02#/xpR0Q7Ťc.:#xvJM<.JLwM{{i $.7`#`$ttw)(<.JLwM{{i |Cch;MMI*ʼ.7`#`$ttw)(<.JLwM{{i 厼.7`#`$ttw)(孿wch;MM*Rb7`4LiHttw)(bJLwM{{i b7`4NUch;MrF	NUch;Ms i%X˦;HD4݀ҩ .:3Y(D4݀Jt~8-^02#/xpR0Q77`#`$4݀Jt`e@G@^`n4݀Jt`e@G@^`n4݀Jt`e@G@^`n-02#/xpR0Q77`#`$-02#/xpR0Q77`#`$j4݀Jt`e@G@^`n4݀ҩ1 d`e@G@^`n02#/xpR0Q77`#`$fyҐ202#/xpR0Q7Ү	H-M4ch;M`I.)#.:#xv6)`e@G@^`onF%1 `-O!#M4ch;M`1<7`#`Ґ202#/xpSI54݀JcJ@˦;M$cv6))#.:4X-O#M4ch;M`1>܍7`#`Ґ202#/xpSI5R4݀JcJ@˦;M$d(v6))#.:4X-شlSRF]14t
i&[0߱FLwM{{wJAmK ƔLwM{{wti ƔLwM{{ISѥ d`e@G@^`onF% Cch;MM4`e@G@^`onF%1 `-.:#xv6))l]nF%1 d`e@G@^঒kwJcJ@˦;HD;LwM{{I4݀JcJ@[L?iWx4ch;M`b)#.:4\i 4݀JcJ@˦;M$jx˦;M$ץ]`Ґ0دZU6))#.:#pY38(Wx4ch;4t
i&v6))#.Y]RF]14t
F
&lR M4ch;Mm]nF%1 d`e@G@^`nn8˦;HD4݀JcJ@[o,Gtw)M4Amť]`Ґ202#/xpR0Q7i ƔLwM{{I@_iWx4ch;M`wch;MqlSRȶx˦;M$ץ]`Ґ0KiWx4ch;MdiHttw)M]RF]14t
i&v6)p!]14t
F
&lSRˬň:#xv6))#.YaX]nF%1 d`e@G@^`n*KM4ch;Me"atiHttw)MSiWx4ch;Me{`e@G@^঒k7`#`Ґ0Xw]14t
i&v6))ewJcJ@˦;M$-OشlSRF]14t
i&W.wJcJ@˦;HDRF]14t
i&v6)FLwM{{I4݀JA_BѦlSRF]14t
F
&zBҐ202#/xpR0Q77`#`Wb`e@G@^`onF%1 `+P4݀JcJ@˦;HD]RF]14t
i&v6)siWx4ch;M]fLwM{{I4݀JcJ@UQlSRF]14t
i&Wu{iHttw)(WxZU6))#.:4X*-* ƔLwM{{IlQ d`e@G@^঒k7`#`     v/%wx   |  3  ߇I*]14t
F
&lRP$ttw)(ƛU$s|	NUch;MM ZMTҐ202#/xpR0Q77`j7ϥRcJ@˦;HD4݀n,`onF%:IV02#/xpPg~IV02#/xpR0Q77`4H,VK獀Jt`e@G@^`on:#xvJ%Xˤ-
&I)#.:c*_<lSc.:#xv :i%X˦;HD4݀JAcp߄iHttw)(ƛU$=T$ttw)(ƛ 9N6))#.:#xv ;)%1 d`e@G@^`on 8I*]14t
F
& ,hSҩ1 d`e@G@^`on8I*]14t
F
& ,YSJcJ@˦;HD4݀kˑ d`e@G@^`onF% gSJcJ@˦;HD4݀lSRF]14t
F
& -RG`$ttw)(ƛ <\)#.:#xvJԬyN6)JLwM{{i Q84ch;MM Z.FLwM{{i מo6)JLwM{{i ]$ttw)(ƛU$'~ d`e@G@^`oniT\~IV02#/xpR0Q77`#`\WLwM{{i %PZi%X˦;HD4݀JAj7ϥRt`e@G@^`onro6)JLwM{{i Xپ}*RF]14t
F
& -k#J@˦;HD4݀ҩ ;JLwM{{iRAku7 %X˦;HD4݀lSRF]14t
F
& -l`$ttw)(ƛ Sҩ1 d`e@G@^`onPyN6)JLwM{{i XQ84ch;MM Z_.FLwM{{i 1y0Q77`#`Ґ202#/xpP `e@G@^`onF%:IT ƒUch;MM ,`e@G@^`onF%:IT `e@G@^`onF%:ITq	NUch;MM Z)%1 d`e@G@^`on׆r4ch;MM`FLwM{{I4݀JAe߄iHttw)lR3`Ґ202#/xpSI5ƛ /6))#.:#}*5`Ґ202#/xpR0Q7Ү@]$nF%1 d`e@G@^,)#.:4^wJAd^_<lSRF]14t
i&v BGtw)lSRF] E0Q7Ү	LiHttw(&`Ґ202#/xpSI5ƛ o4ch;MqlR(#J@˦;HDJ% /6))#.:4^wq	LiHttw)M YZ ƔLwM{{I4݀q	LiHttw)M Y< ƔLwM{{I4݀q	LiHttw)M Y ƔLwM{{I4݀ˑ d`e@G@^঒k7`#`UHJq	LiHttw)M UJq	LiHttw)M Wh2lSRF]14t
i&v ܹRF]14t
i&v6)r)%1 d`e@G@^঒k7`\8q	LiHttw)M YzRF]14t
i&v6))|U&4ch;MM XF7ᤕc.:#xv6)C~IV02#/xpR0Q77`#`X7ᤕc.:#xv6)	|U&4ch;MM X7ᤕc.:#xvJaҐ202#/xpSI5ƛ	H,K獀JcJ@˦;M$ץ]`_>I)#.:#xv ~%%1 d`e@G@^`o]`d߆Uch;MMi%X˦;HD4݀ҩ K/J%X˦;HD4݀K ƔLwM{{i 
N6))#.:#xv lSc.:#xv I)#.:4\i 
	N6))#.:4\i 
r4ch;MqlR
0Q77`#`Ґ202#/xpP%G)%1 d`e@G@^`on084ch;MM V2lSc.:#xv RcJ@˦;HD4݀k#)%:IV02#/xpR0Q77`Zeˑ d`e@G@^`onF% 9;)#.:4^wJAla]`Ґ202#/xpR0Q7`e@G@^`o]`Ґ0U6))#.:#p[Gtw)(Wx4Alaa]`Ґ202#/xpR0Q7lSRF]14t
i&v ׳|	LiHttw)(Wp[XFLwM{{I4݀JAmwRF]14t
i&v6)i߄iHttw)Ms|	LiHttw)(Wp[~FLwM{{IJ% W;)#.:#}* o6))#.:4\i g)x4ch;M-`Ґ202#/xpSI5ƛ ;)#.:4\i ڈ4ch;MzU6)<lSRF]14t
i&*iq84ch;Mq -`Ґ202#/xpSI5ƛ ySJcJ@˦;M$n٨yN6))#.:4\i e84ch;Mq -#J@˦;M$nF% ^qMqlSRF]14t
 yN6))#.:4\i o84ch;Mq -`Ґ202#/xpSI5ƛ SJcJ@˦;M$nyN6))#.:4\i k{Ґ202#/xpSI5ƛ	K      |Öx=!ʛ  3  ~vJƔLwM{{,>{7`#`$ttw)(ĒX˦;HD4݀ҩ:IT&FU'I*]14t
F
&^oI*]14t
F
&lR#M*RF]14t
F
&౏4݀Jt`e@G@^`n #M*RF]14t
F
&2oI*]14t
F
&lR
4MM*c.:`߆Uch;MM*4`e@G@^`onF% 4݀ҩ1 d`e@G@^`n4`e@G@^`onF% K#M4ch;MQ.FLwM{{i \JLwM{{i 6#/xpSI5ƛU&4AZ˚IV02#/xpR0Q77`#`Vt4wM{{i ƔH*pv6))#.:#pX|nF%1 d`e@G@^`n#J@˦;HD4݀JA[ˑlSc.:#pVriHttw)(ƛU$/.F	NUch;MbiHttw)(ƛ	H,Sqch;MM4߄i %X˦;HD~ d`e@G@^`oniTZ}F	NUch;MjniT$ttw)(ճ4݀ҩ:IV02#/xpR0Q7,`e@G@^`onF%:IT~ d`e@G@^`oniTX(ƛU&4ch;_~lSc.:#pXniT$ttw)($I*]14t
F
&I<lSc.:#xv ?~I)#.:#pX|nF%1 d`e@G@^`n7h;MM4Acui %X˦;HD4.FLwM{{iRAjPnF%:IV02#/xpR0Q7iHttw)(ƛ	H-D7c.:#xv6))j|RF]14t
F
&lRTh:#xv6)JH-O/h;MM*RF] ~\7`#`$ttw)(r4ch;MMoˑlSRF]14t
F
&d~\7`#`Ґ202#/xpR0Q7nF%:IV02#/xpR0Q7߄i %X˦;HD~ d`e@G@^`oniTZ
&IJLwM{{;JLwM{{i lI*]14t
F
&I'߄i %X˦;HD'~ d`e@G@^`oniTZ?.F	LiHttw)(sI*]14t
F
&lRZ[Ґ202#/xpR0Q77`4H-|/#J@˦;HD4݀JAk}@G@^`onF%1 d`e\v6))#.:#p\WLwM{{i %P\g	NUch;MM \WLwM{{i %P\lSc.:#p\WǱLwM{{i %PZ.i%X˦;HD4݀JAlg]`Ґ202#/xpSI54݀JcJ@˦;M$eX˦;HDJ%1 `-#J@˦;M$nF% 6<P)#.:#}* #J%1 d`e@G@^`nccҐ202#/xpR0Q7Ү	H-?n4lSRF]14t
F
&00Ү	LiHttw)(ٝr4݀JcJ@˦;M$eҐ202#/xpSI5ƛ	H-_#M4ch;M`:~\7`#`Ґ202#/xpSI5cJ%1 d`e@G@^`nnv6))#.:4X-Wc.:4^wJcJ@Y]`Ґ202#/xpSI5ѿҐ202#/xpSI5ƛ	H,Ү	LiHttw)(ɗv6))#.:4X-4lSRF]14t
F
&඄;)#.:4\i opI5Wx4ch;߄iHttw)lRkҐ202#/xpSI5ƛ	H-4lSRF]14t
F
&;)#.:4\i Qr4݀JcJ@˦;M$hҐ202#/xpSI5ƛ	H-#J@˦;M$nF% ƾ\)#.:4\i ;M$nF%1 d`ej7v6))#.:4X-_#M4ch;M`\)#.:4\i }r4݀JcJ@˦;M$m[Ґ202#/xpSI5ƛ	H,>\7`#`Ґ202#/xpSI5Ґ202#/xpSI5ƛ	H,nqch;MqlSR߿v6))#.:4X,)#.:#}* Ͽv6))#.:4X,{Ү	LiHttw)g_߆wJcJ@˦;M$
Tch;MqlSRٿҐ202#/xpR0Q7Ү	H,lMlSRF]14t
ʇv6))#.:4X,Ү	LiHttw)e߄iHttw)lR0`Ґ202#/xpSI5ƛ J%1 d`e@G@^`n,ϗ#M4ch;M`z;M$nF%1 d`e)#M4ch;M`}yr4ch;MqlR
\7`#`Ґ202#/xpSI5#J@˦;M$nF% 02#/xpSI5ƛ	LiH
r4ch;MqlR
#/xpSI5ƛ	LiHt{h;MqlSRF] #J@˦;M$nF% #M4ch;M`{#M4ch;M`    	  #   "*              3  correctQ a1 _root incorrectClip play correctClip    I !           N R            N R  	 '    
 X#FAp  	 3 hh      # 
  "*              3  correctQ a2 _root incorrectClip play correctClip    I !           N R            N R   Õ     XFp 	 3 hh      #   "*              3  correctQ a3 _root incorrectClip play correctClip    I !           N R            N R 
  F @     X#Jp  
 3 hh      #   "*              3  correctQ a4 _root incorrectClip play correctClip    I !           N R            N R   F 	$      M1 @3       ( title   m 	&    | 0  3        ( answer1   +" 	&     0  3        ( answer2   +#$ 	&     0  3        ( answer3   +#  	&     0  3        ( answer4     	'    .? m0  3        ( question   @    H    u}rΥP 333 r4 B ,s 2k *&X f`:)        f#     :FtYm]:  0    E    WdI@P,KmY?;$RNE n   &  a    X@     p8>    n_b(N'6AS5,$  XY4-.1i l[ (<1h) [Zv@_Y>hаgw  )I$I*I$HȺ+QB@  dba =qR`b;r !s Ki|Aby"x( 8P_Z<| lA0R``t(BLܴAZi PUlON-i/̾_Q|? `.`h| `<\^I;>&Mh.y kҁA|n^/"*iq	phQI%Z/陛JI"}E0 aq]2 BRˢ4+CI8Lryl( ~/ھY|܂(xȢI"Z)$dcdM  Z@&H	%Ft{- wgX{7Py՟fm Zǀ{Vq?FO:=%9@.:iѦM4 402####"fOvۻ;;;; 2VDݝݝCC
$M$cXB+
2t,hfd$+ŅP.T[P1Qf@MʅXT Bp\                                                                                              [  X                                                                                               ?0   Tahoma   /    cy$7[] R lMl3lKxXZ*OOCn{
)(.-͕l繦=K ڎlbce3:Y{KDRr)4os7qD	gn4Ҫ'*KmP'S5íLvHe5! 	Z1pR[WecE8핎 Jm6mͧCCʔ6S i v$yzʠ)9h3,Iast ij+1Ia v`Ruem& &zf鷛`
!JeW=i9&L =L0@Vtdܸ-m K(r%Dps7D1k@sv@n j0 w0qKcb?(؝`̩̗Q)t o6%Df\i5I^Rwb{Wڙ*/&4HeG(`, /nAj9HlN! C E I N O R T (    h> p  
    (PAc@ 5    h	WD  
 3 ||\E85	`5cT%yǀ  %    e!-Wo
P  3  35b9Re+9m@ 5    h	WD  
    ||\E85	`5cT%yǀ y   &  }    X@  `~4ᮀ}~|t  4A?.D<1   F\ܾA.2c09 [SX @'a+t\ A
79Oq jaHhf`e)$I$(Hȋ 7/2 8Ԁ&wUw4[Xք 
)hH-/VPx,;j_3MrTr+P @Â@Dg  54vAF5X1aajDi\TT2o7S?U.                    X@bf^	H                                                                                            n  X                                                                                                     9   Z2     Z2  Z2     Z2              _root   nextQ R        this   gotoandStop R              	  ! % D   ?    @   _@ F  j
jJm   .N'37  .N'3Tt  .N'3rL  .N'3$  .N'3  Ѳ'1J(	  Ѳ'1,
  Ѳ'1܎  Ѳ'-*Ў  Ѳ'-20  Ѳ'-m9  Ѳ'0<  Ѳ'0{  Ѳ'0^  Ѳ'0@UĎ  Ѳ'0"ל  Ѳ'0Yt  Ѳ'3L  Ѳ'3](     @  jj	Jn
@  jj	Jn>Tb@  j
jJnOT@  jj	JniT@  jj	Jn@  jj	Jfqx@  j
jJ_@@ @ @     .N'37 .N'3Tt .N'3rL .N'3$ .N'3 Ѳ'1J( Ѳ'1,	 Ѳ'1܌
 Ѳ'-*Ќ Ѳ'-20 Ѳ'-m9 Ѳ'0< Ѳ'0{ Ѳ'0^ Ѳ'0@UČ Ѳ'0"ל Ѳ'0Yt Ѳ'3L Ѳ'3](  X @  @   X @  @   X @  @   X @  @   X @  @   X @  @   X @  @   X @ @ @ @ @ @ @ @ @ @ ?       Ք$ @      6 !  correctClip I  " &  a    X@    @  #5 i.'Dٍa%1:'	`L(3@fӁ 2>\@ [ZfK ˅9Ѡ II$d^/&CCT !d"v L Ag00je#G * xH 3#@ Tބ8X USWu]oJd)UIE"7
pp_@0YxHA`f  5'/ WzYE.Da"R'ng!4ݓLQZP4"Ƈ  0B4 3v p<a 𓛷 F ovYƀ08(B!!Bs5kZֵλ9sֵoֵkH;q HPPQ               ^ѶvYX                                                                                            i  X                                                                                                  X                                                                                               ,   # hp  
   d 
eL1T<d!+@ +   $ h   	 3 ||	hꤢ h  $   % e7o
P  3  35mst|c9mGC +   & h   	    ||	hꤢ h   ' &  }    X@   >xw^~ 4l @,  |}ĤQO!cRкOsqx YaL᳈<4 [$;d %3XhqLp8rȘAp1m3!@׋ ?  ★*HRIhIVR6p %{rhaQEJ(~ߩ
}'SI$H
xEd
x a^FAq)^>۫ϣ7̯c4p .bNs
`BL51)B
"B	Xd/?/gRrVOAY       Eb\D                                                                                            `  X                                                                                                  X                                                                                               <   (  / $  8%   &  8%   $  8           (     '       ) W 	  3||h 	  * % D   ?    @    @ F  B!;Bm   Ѳ'3d  ѳhaJ  ѳha78  ѳh`3  ѳh`/؏  ѳh`^,(	  ѳh`#(x
  ѳhg$ȏ  ѳhg!  ѳh^u  ѳh^nf  ѳh]X   ѳh]I@  ѳh]:  ѳh\+  Ѳ'08   "  @  B!;Be(x@  B!;B\[$@  B!;B]S`@  B!;B^o`@  B!;B^xF  BƽPj	#   Ѳ'-  Ѳ'-KP  Ѳ'-$  Ѳ',,  Ѳ',3p  Ѳ',_:Ў  Ѳ'0  Ѳ'3<  Ѳ'3V  Ѳ'3  Ѳ'3~YĎ   Ѳ'3`ۜ!  Ѳ'3C]x"  Ѳ'3$_4@  BƽOcU@  BƽOby@  BƽO[@@  BƽOZ9F@  BƽPXv $ # X @ $ @ $ # X @ $ @ $ # X @ $ @ $ # X @ $ @ $ # X @ $ @ $ # X @ $ @ $ # X @ @ @ @ @ @ @ @ @ @ @ @ ?    %   jD$ ( ( D$ + ) 5 @      6/ * Р incorrectClip @   
         / ?    F  T  S 2   + pL$0  3 '&XR JV${G  + 7@  T  S@  T  0S@  T  S@  T  S@  T  VS@  T  S@  T  S@  T  S@  T  TS@ @ @ @ @ ?    /   , h\	<  
  3ll
= jzYoB@  %   - dm9  3  35`>dm9bc9^  /   . h\	<  
    ll
= jzYoB@ T   /  / ,  C-   .  C,  C-         currentQ               /     '     /  @   