CAIE S1 (Statistics 1) 2020 Specimen

1 Th fb low ing b ck te b ck stem-ad leaf il ag am sw stb a lsalaries \(\mathbf { 6 }\) agp \(\mathbf { 6 } \mathbf { 9 }\) females adgn ales. Key 4 Q 3 m eas ( st \(\mathbf { o }\) females an of \(\mathbf { o }\) males.

1. Fid b med ara d b ɛ rtiles \(\mathbf { 6 }\) th females' salaries. Yo are gie \(n\)th \(t\) th med an salary \(\mathbf { 6 }\) th males is \(\boldsymbol { \otimes } \rho\) th lw er \(\mathbf { q }\) rtile is \(\boldsymbol {
   ) } \boldsymbol { \theta }\( ad th \)\mathbf { p }\( r e rtile is
   )50
2. Drawap ir d ad wh sk rpos in a sig ed ag amo to g id b lw to rep esen th d ta. [β
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2 A sm mary \(\mathbf { 6 }\) th sp esl, \(x \mathrm { k }\) lm etres \(\boldsymbol { \rho } \mathbf { r b }\), \(\mathbf { 0 } 2\) cars \(\boldsymbol { \rho }\) ssig a certain \(\dot { \mathrm { p } } \mathrm { ng }\) th fb low ig if o matin $$\Sigma ( x \oplus ) = 3 \mathrm { a } \quad \mathrm {~d} \quad \Sigma ( x \oplus ) ^ { 2 } = \mathbb { t }$$ Fid b riance 6 th sp ed ad \(n\) e fid b vale \(6 \Sigma x ^ { 2 }\). [4]

3 A b clb sed 6 p p rb ck ad 2 h r ck b to Mrs Ho . Sb cb es 4 6 tb se b at rach to take with b r o b id y. Th rach \& riable \(X\) rep esen s tb m br \(\mathbf { b }\) p \(\mathbf { p }\) rb ck b sh cb es.

1. Sth that th p b b lityt \(\mathbf { h }\) tsb cb es extlye perb clb is \(\frac { 3 } { 14 }\). [R
2. Draw up b pb b lityd strib in tab e fo \(X\).
3. Yu reg it h t \(\mathrm { E } ( X ) = 3\) Fid \(\operatorname { Var } ( X )\).

4 A \(\boldsymbol { \rho }\) trb station fid th tits \(\mathbf { d }\) ily sales，in litres，are \(\mathbf { n }\) mally \(\dot { \mathbf { d } }\) strib ed with mean ad stad rd d \(\dot { \mathbf { v } }\) atin \(\quad 0\)
（a）Fid 0 may dy 6 th \(\mathbf { y }\) ar（B d \(\mathbf { y }\) ）th d ily sales can b eq cted to e区 eed \(\boldsymbol { \theta }\) litres． Th d ily sales at an \(\mathbf { b } r \mathbf { p }\) trb station are \(X\) litres，we re \(X\) is \(\mathbf { n }\) mally \(\dot { \mathbf { d } }\) strib ed with mean \(m\) ad stad rd iv atird \(\quad t\) is g it h \(\mathrm { t } \mathrm { P } ( X > 0 = \mathbb { 0 }\)
（b）Fid by le \(6 m\) ．
(c) Fid th p b b lity th t d ily sales at th s p trb station ex eed \(\theta\) litres \(\mathbf { n }\) fewer th n 266 rach lyc \(b\) end \(y\).
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5 A fair six sid dl e,w itlf aces mark dress s ther im imes.

1. Use ara \(p\) in matin of id b pb b lity b ta 3 s ob ain of ewer th rㅇs imes. [4]
2. Js tifys se 6 th ap ox matin pe rt (a). Ora \(\mathbf { h }\) b roccasity he same \(\dot { \mathbf { d } }\) e is th \(\boldsymbol { w }\) ep ated y il a \(\mathbf { 3 } \mathrm { sb }\) aie d
3. Fid b pb b lity b tb ain g ʒ eq res fewer th \(n\) st \(h\) s.

6 Ag \(\mathbf { \Phi }\) of ries trac ls to b airp t irt wd axis, \(P\) ad Q.E acht ax cart ak \(\boldsymbol { \mathcal { C } }\) sseg rs.

1. Th 8 fried dive th msele s in o two gp 6,4 日 gp fo tax \(P\) ad o gp fo tax \(Q\),w ithlo il aralt rae llig it te same tax. Fid b m brd dl fferen way inw hick his carb de .
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   \includegraphics[max width=\textwidth, alt={}, center]{1fef5f2c-b375-4be2-b8a1-c30136bd0063-11_301_478_223_1142} Each tax can tak \(1 \boldsymbol { \rho }\) sseg r in th fro ad \(3 \boldsymbol { \rho }\) sseg rs in th \(\mathbf { b }\) ck (see \(\dot { \mathbf { d } }\) ag am). Mark sits in th
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2. Fid b m brd d fferen seatig rrag men s th tare \(\mathbf { w }\) sibefo th of ried . [4]

7 Bag \(A\) ch ais \(4 \mathbf { b }\) lls \(\mathrm { m } \quad \mathbf { b }\) red \(2,4,58\) Bag \(B\) ch ais \(5 \mathbf { b }\) lls \(\mathrm { m } \quad \mathbf { b }\) red 1,3688 Bag \(C\) co ais 7 b lls m b redram a b \(l l\) is selected \(t\) rach frm eaclb \(g\)

• Ed \(n X\) is 'ed ctlyt wo th selecteb lls \(\mathbf { h }\) th same m br'.
• Ed n \(Y\) is 'tb b ll selected rm bag \(A \mathbf { h }\) sm br4.
  1. FidP (X).
  2. Fid ( \(X \cap Y\) ) aid \(\mathbf { n }\) ed termin wh ther or \(\mathbf { n }\) even \(\mathrm { s } X\) ad \(Y\) are id \(\mathbf { p } \mathbf { d } \quad \mathrm { h }\). [B
  3. Fid the p b b lity th t two \(\mathbf { b }\) lls are \(\mathrm { m } \quad \mathbf { b }\) red \(2 \dot { \mathrm {~g} }\) n th t ex ctly two \(\mathbf { 6 }\) th selected \(\mathbf { b }\) lls h \& th same m br.

If B e th follw ig lin dpg to cm p ete th an wer(s) to ay q stin (s), th q stin \(\mathrm { m } \quad \mathbf { b } \quad \mathrm { r } ( \mathrm { s } )\) ms tb clearlys n n