CAIE S2 (Statistics 2) 2020 Specimen

1 Leat s frm a certain tro tree \(\mathbf { h }\) leg \(\mathbf { b }\) th t are \(\dot { \mathbf { d } }\) strib ed with stad \(\operatorname { rd } \mathbf { d } \dot { \mathbf { v } }\) atio \(\mathbf { Z }\) cm. A rach sample 6 6 th se lead s is tak n ad the mean leg \(\mathrm { h } \mathbf { 6 }\) th s samp e is fo d to b © cm .

1. Calch ate a 90 cf id \(n\) e in erd \(l\) fo th \(p p\) atim earl eg \(h\)
2. Write d n th p b b lity th t th wh e 6 a \(9 \%\) co id n e in ery l will lie b low th p atim ean

2 Describ b iefly to s e rach m b rs to cb e sampe \(\mathbf { b } \boldsymbol { \mathbb { I } }\) std ns frm a \(\mathbf { g }\) ar-g \(\mathbf { p } \boldsymbol { \mathbf { 6 } } \varnothing\) ste ns.

3 Th m brg calls receie d at a small call cen re \(\mathbf { h }\) s a Posso id strib in with mean

4 Th lifetimes, in b s, b Lg ie lig b b ad Ee rlw lig b b be tb id pd n id strib in \(\mathrm { N } \left( \mathrm { LS } ^ { 2 } \right)\) adN ( \(\mathrm { L } ^ { 2 }\) ) resp ctie ly.

1. Fid th pb b lity th t to to al 6 th lifetimes 6 fie rach ly cb en \(L \mathbf { b }\) ie \(\mathbf { b }\) b is less th \(\mathrm { HB } \quad \mathrm { Ch } \quad \mathrm { S }\).
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2. Fid th pb b lity th tth lifetime 6 a rach lycb en En rlw b b is at least th ee times th \(t\) 6 a rach lyc b erL b ir b b

5
\includegraphics[max width=\textwidth, alt={}, center]{8f62635a-2998-468f-8017-0db050d612be-08_270_648_251_712} Th diag am sh s th g a to th pb ab lityd nsityf n tiff, to a rach \& riab e \(X\),w b re $$f ( x ) = \begin{cases} \frac { 2 } { 9 } \left( 3 x - x ^ { 2 } \right) & 0 \leqslant x \leqslant 3
0 & \text { otherwise } \end{cases}$$

1. State th \& le \(6 \mathrm { E } ( X )\) aff id \(\operatorname { Var } ( X )\).
2. State th le \(6 \mathrm { P } (
   ) \leqslant X \leqslant 4\(.
3. Giv it h \)\mathrm { P } \left( 1 \leqslant X \leqslant \mathcal { P } = \frac { 13 } { 27 } \right.\(, f idP \)( X > \mathcal { P }$.

6 At a certain b \(\dot { p }\) tal it was fd th \(t\) th \(p\) b b lity th \(t\) ap tien \(\dot { d } d \mathbf { p }\) arrie fo an ap \(n\) men was Q. Th b \(\dot { p }\) tal carries t sm ep icity in th th t thspb b lity willb red ed Tby wisht \(d\) est wh th \(r\) th \(p\) icityh swo k d A rach sample 6 B ap \(n\) men s is selected ad th \(m\) brg tien sth td \(\mathbf { p }\) arriw is \(\mathbf { p }\) ed Th s fig e is s ed œ arry a test at th \% sig fican e lew l.

1. El ain wh b test is a -tailed do tate siu tabeh lad ltera tir bes. [R
2. Use abm ial d strib in to fid to critical rego ad fid th p b b lity \(\mathbf { 6 }\) a Tr I erro . [\\(
3. If act \)3 \boldsymbol { p }$ tien su 6 the Oh arrie . State the co lo ind th test, e ain gy ras wer.

7 Th mean weig 6 bg 6 carrb s is \(\mu \mathrm { klg }\) ams. An is \(\mathbf { p }\) cto wish s to test wh th \(\mathrm { r } \mu = 20\) He weig a ranch sampe 6 tb \(g\) an \(s\) resh ts are sm marised \(s\) fb low \(s\). $$\Sigma x = 430 \quad \Sigma x ^ { 2 } = 0$$ Carryo the test at the to sig fican e lee 1 . 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