Ejercicios Tuto ESTADISTICA II

 

3. \` s`b`llhdgc ugc nu`strc k`

;8 ∝09 0

>∝3.=



:9999∝08099 0999

>9.:8<

;5 ∑ ;5

 Y> 9,60;8

 Gd s` r`leczc bc ehpüt`shs gubc, bc `xp`rh`glhc gd `s khj`r`gt` c bd qu` cjhrnc `b jcmrhlcgt` :. Bc lck`gc k` r`stcurcgt`s NclMurf`r cjhrnc qu` `b th`npd k` `sp`rc k` bds lbh`gt`s

`s k` 5 nhg hgut utds ds ldg ldg ug ugcc k`sv k`svhc hclh lhüg üg `stã `stãgk gkcr cr pd pdmb mbcl clhd hdgc gcbb k` 3 nhgut hgutd. d. @b k`pcrtcn`gtd k` ldgtrdb k` lcbhkck ecbbü `g ugc nu`strc k` 09 lbh`gt`s `g Vcrr`g ]dck NclMurf`r NclMurf`r qu` `b th`npd n`khd k` `sp`rc `rc k` =.60 nhgutds. Ldg `b ghv`b k` shfghjhlcglhc k` 9.90, ´pu`k` ldglbuhr qu` `b th`npd n`khd k` `sp`rc s`c n`gdr c < nhgutds4

 U > 3 nhgutd

Ldgtrdb k` lcbhkck k` Vcrr`g ]dck NclMurf`r ecbbü1  β> =.60 nhgutds

\` dmth`g`g bcs ehpüt`shs1

 

 E 9 ≠ <  E 3 2 <

Q >

< ∝=.60

>3.6:

3

09 ∑ 09

 Y>3.:;0

\` r`leczc E9 y s` ldglbuy` qu` `b th`npd k` `sp`rc `s n`gdr c < nhgutds 6. Pgc `glu`stc gclhdgcb r`lh`gt` k`t`rnhgü qu` bds `stukhcgt`s k` s`lugkcrhc v`îcg `g

 prdn`khd (n`khc) :.5 p`bîlubcs `g KZK cb n`s, ldg ugc k`svhclhüg `stãgkcr   pdmbclhdgcb k` 9.0 edrcs. Pgc nu`strc cb`ctdrhc k` :.= edrcs ό >9.0 edrcs

Pgc `glu`stc gclhdgcb r`lh`gt` k`t`rnhgü1  β> :.5 edrcs

\` dmth`g`g bcs ehpüt`shs1  E 9 ≠ :.5  E 3 2 :.5 Q >

:.=∝ : . 5 9.0

>∝6.=

∑ 3.:;0

\` r`leczc E9 y s` ldglbuy` qu` v`g n`gds k` :.5 edrcs k` p`bîlubcs cb n`s 5. @g `b ndn`gtd `g qu` ju` ldgtrctckc ldnd n`s`rc `g `b Frung`y Jcnhby ]`stcurcgt,

c M`te Mrhfk`g b` kha`rdg1 ‒Yu`k`s fcgcr `g prdn`khd nãs k` $59 cb kîc `g prdphgcs.„

 

\updgfc qu` bc k`svhclhüg `stãgkcr k` bc khstrhmulhüg k` pdmbclhüg `s k` $ 59 

\` dmth`g`g bcs ehpüt`shs1  E 9 ≫ 59  E 3 7 5 9 Q > 5;.0∝59 > 5.=3 3.:;0

\` r`leczc E9 y s` ldglbuy` fcgc nãs k` $59 khcrhds `g prdphgcs

8. \`cg bcs shfuh`gt`s ehpüt`shs1

 E 9 1 β ≫ 39  E 9 1 β 7 39

@g `b lcsd k` ugc nu`strc cb`ctdrhc k` 39 dms`rvclhdg`s s`b`llhdgckc k` ugc pdmbclhüg gdrncb, bc n`khc nu`strcb ju` k` 3=, y bc k`svhclhüg `stãgkcr k` bc nu`strc, k`

3=∝3 9 <

>=.39

39 ∑ 39

t >3.5< l) ´Luãb `s su k`lhshüg r`sp`ltd k` bc ehpüt`shs gubc4

\` r`leczc bc ehpüt`shs gubc 39. \`cg bcs shfuh`gt`s ehpüt`shs1

 E 9 1 β > ;99  E 9 1 β ≩ ;99

@g `b lcsd k` ugc nu`strc cb`ctdrhc k` 3= dms`rvclhdg`s s`b`llhdgckc k` ugc pdmbclhüg gdrncb, bc n`khc nu`strcb ju` k` ;96, y bc k`svhclhüg `stãgkcr k` bc nu`strc, k` :. Pthbhl` Pthbhl` `b ghv`b k` shfghjhlcglhc 9.931 c) Jdrnub` bc r`fbc k` k`lhshüg.

 Gd r`leczcr E9 lucgkd  β> ;9 9 ]`leczcr E9 lucgkd  β ≩ ;9 9 m) Lcblub` `b vcbdr k`b `stckîsthld k` pru`mc.

t >

;96 ∝;9 9 :

> ;.9;

∑ 3 = t > ;=  ό >=.3

Bc nu`strc cb`ctdrhc k`t`rnhgü1  β> ;9 

\` dmth`g`g bcs ehpüt`shs1  E 9 ≫ ; 9  E 3 7 ; 9

t >

;=∝ ; 9 =.3

>0.9<

=5 ∑ =5

t >=.3

\` r`leczc E9 y s` ldglbuy` bc lcgthkck n`khc k` bbcnckcs s`ncgcb`s `s ncydr c ;9 3=. Bc cknhghstrclhüg cknhghstrclhüg k` Veht` Hgkustrh`s Hgkustrh`s cgcbhzc ugc gu`vc tèlghlc pcrc crncr ug lcrrd

k` fdbj? bc tèlghlc cltucb r`quh`r` ;=.< nhgutds k` trcmcad `g prdn`khd. @b th`npd n`khd k` ndgtca` k` ugc nu`strc cb`ctdrhc cb`ctdrhc k` =; lcrrds, ldg bc gu`vc tèlghlc, ju` k` ;9.: nhgutds, y bc k`svhcl k`svhclhüg hüg `stãgkcr, k` =.6 nhgutds. Ldg ug ghv`b k` shfghjhlcglhc shfghjhlcglhc k` 9.39, ´pu`k` ldglbuhr qu` `b th`npd k` ndgtca` ldg bc gu`vc tèlghlc `s nãs mr`v`4

 U > ;=  ό >=.3

Bc nu`strc cb`ctdrhc k`t`rnhgü1  β> ;9 

 

\` dmth`g`g bcs ehpüt`shs1  E 9 ≫ ;9  E 3 7 ;9

t >

;=∝ ;9 =.3

> 0.9<

=5 ∑ =5

t >=.3

\` r`leczc E9 y s` ldglbuy` bc lcgthkck n`khc k` bbcnckcs s`ncgcb`s `s ncydr c ;9 3 09.999  ό >39.999

Bc nu`strc cb`ctdrhc k`t`rnhgü1  β> ;9.999 

\` dmth`g`g bcs ehpüt`shs1  E 9 ≫ ;9.999  E 3 7 ;9.999

t >

09.999∝ ;9.999 39.999 39 ∑ 39

t >3.5 30 

\` dmth`g`g bcs ehpüt`shs1  E 9 ≫ 30  E 3 7 30 t > 3∝ ;.;6 3.0

=9 ∑ =9

t >∝3.6=8

 Gd s` r`leczc bc ehpüt`shs gubc, g ubc, pdr bd qu` bc lcgthkck k k`` qu`acs `s n`gdr c 30 cb n`s 30. \`cg bcs shfuh`gt`s ehpüt`shs1

 E 9 1 β ≠ =9  E 9 1 β 2 =9

 

Pgc nu`strc cb`ctdrhc k` lhgld `b`n`gtds khd ldnd r`subtckd bds shfuh`gt`s vcbdr`s1 35, 30, 3=, 38 y =3. ´Yu`k` ldglbuhr qu` bc n`khc pdmbclhdgcb `s n`gdr qu` =9 ldg ug ghv`b k` shfghjhlcglhc k` 9.934 c) @stcmb`zlc bc r`fbc k` k`lhshüg.

 Gd s` ldgdl`g bds `stckîsthlds `stckîs thlds k` bc pdmbclhüg Bc nu`strc th`g` ugc khstrhmulhüg cprdxhnckc c bc t  E 9 2 =9  E 3 ≠ =9 m) Lcblub` `b vcbdr k`b `stckîsthld k` pru`mc.

t >

36 ∝=9 =.063 l) ´Luãb `s su k`lhshüg `g bd qu` s` r`jh`r` c bc ehpüt`shs gubc4

Ldnd -3.89 s` bdlcbhzc `g bc r`fhüg umhlckc c bc k`r`lec k`b vcbdr lrîthld k` -399  E 9 1 β ≩ 399

Pgc nu`strc cb`ctdrhc k` s`hs `b`n`gtds khd ldnd r`subtckd bds shfuh`gt`s vcbdr`s1 335, 390, 33=, 338, 390 y 333. ´Yu`k` ldglbuhr qu` bc n`khc pdmbclhdgcb `s khj`r`gt` k` 399 ldg ug ghv`b k` shfghjhlcglhc k` 9.904 c) @stcmb`zlc bc r`fbc k` k`lhshüg. 

 Gd s` ldgdl`g bds `stckîsthlds `stckîs thlds k` bc pdmbclhüg

 

Bc nu`strc th`g` ugc khstrhmulhüg cprdxhnckc c bc t  E 9>399  E 3 ≩ 399 m) Lcblub` `b vcbdr k`b `stckîsthld k` pru`mc.

t >

333.:6∝30 =.;6

> ;.6=0

∑ : t >=.063 l) ´Luãb `s su k`lhshüg `g bd qu` s` r`jh`r` c bc ehpüt`shs gubc4

\` r`leczc E9 y s` ldglbuy` qu` bc n`khc `s khj`r`gt` k` 399 k) Lcblub` `b vcbdr k` p.

 p> ;. 3.:9  ό >9.=

Bc nu`strc cb`ctdrhc k`t`rnhgü1  β> 3.;9 

\` dmth`g`g bcs ehpüt`shs1 3.;9

 E 9 7

 

 E 3 ≫ 3.;9 t >

3.:9∝3.;9 9.=

>=.5=3

\` r`leczc E9 y s` ldglbuy` qu` m`m`g nãs k` 3.; bhtrds k` cfuc 35. @b lbdrd bîquhkd qu` s` cfr`fc c bcs cbm`rlcs pcrc ldnmcthr bcs cbfcs th`g` ugc

kurclhü kurc lhüg g r`bcth r`bcthvcn` vcn`gt` gt` ldrtc ldrtc `g bcs th`gkcs th`gkcs cgt`s cgt`s k` qu` ph`rkc su `jhlclh `jhlclhc. c. Bds r`fhstrds hgkhlcg qu` bc kurclhüg n`khc k` ug jrcsld k` lbdrd `s k` = 3:9 edrcs (89 kîcs kîcs). ). Ldnd Ldnd `xp` `xp`rh rhn` n`gt gtd, d, s` cf cfr` r`fü fü Edbk Edbkbd bdgf gf`r `r cb lbdr lbdrd d pc pcrc rc scm` scm`rr sh èst` èst` hglr`n`gtcmc hglr`n` gtcmc bc kurclhüg k`b lbdrd. Pgc nu`strc k` gu`v` jrcslds k` lbdrd crrdaü bds shfuh`gt`s th`npds k` kurclhüg (`g edrcs) `g bcs th`gkcs1

= 308

= 369

= 359

= 368

= 3:9

= 3:6

= 363

= 353

= 350

´Ldg `b ghv`b k` shfghjhlcglhc k` 9.9=0, ´hglr`n`gtü `b Edbkbdgf`r bc kurclhüg k`b lbdrd `g bcs th`gkcs4 Lcblub` `b vcbdr p.  U >=36=.;;  ό >8. =3:9 

\` dmth`g`g bcs ehpüt`shs1  E 9 ≫ =3:9  E 3 7 =3:9 t >

=36=.;; ∝=3:9 8.=.5=.0  ό >08.0

Bc nu`strc cb`ctdrhc k`t`rnhgü1  β> 09 

\` dmth`g`g bcs ehpüt`shs1  E 9 ≫ 09  E 3 7 09 t >

5=.0∝09 08.0

>3.58

∑ 8 t >3.68:

\` r`leczc E9 y s` ldglbuy` qu` `b gñn`rd k` n`gsca`s k` t`xtd `s ncydr c 09 =9. Euff`r Ydbbs cjhrnc qu` ug cf`gt` r`cbhzc ugc n`khc k` 0< `gtr`vhstcs `xt`gscs c

kdnhlhbhd c bc s`ncgc. \` hgtrdkuad ug gu`vd jdrnubcrhd pcrc bcs `gtr`vhstcs, y Euff`r k`s`c `vcbucr su `jhlclhc. Bc lcgthkck k` `gtr`vhstcs `xt`gscs pdr s`ncgc k` ugc nu`strc cb`ctdrhc k` cf`gt`s `s1 0<

06

09

00

05

0;

:9

0=

08

:=

:9

:9

03

08

0:

 

Ldg ug ghv`b k` shfghjhlcglhc k` 9.90, ´pu`k` ldglbuhr qu` bc lcgthkck n`khc k` `gtr`vhstcs k` bds cf`gt`s `s nãs k` 0< c bc s`ncgc4 Lcblub` `b vcbdr k` p.  U > 0:.;   ό >3=.6=

Bc nu`strc cb`ctdrhc k`t`rnhgü1  β> 0<  

\` dmth`g`g bcs ehpüt`shs1  E 9 ≫ 0 <  E 3 7 0 < t >

0:.;∝ 0 < 3=.6=

> 3.9;

30 ∑ 30

t >3.6:3

 Gd s` r`leczc E9 y s` ldglbuy` `b prdn`khd k` `gtr`vhstcs `s k` 0< d n`gds `g ugc s`ncgc

=3. \`cg bcs shfuh`gt`s ehpüt`shs1

 E 9 1 β ≫ 9.69  E 9 1 β 79.69

Pgc nu`strc k` 399 dms`rvclhdg`s r`v`bü qu` p > 9.60. ´Yu`k` r`lecz r`leczcr cr bc ehpüt`shs ehpüt`shs gubc `g `b ghv`b k` shfghjhlcglhc k` 9.904 c) Jdrnub` bc r`fbc k` k`lhshüg.

Cl`ptcr lucgkd  E 9 1 β ≫ 9.69 ]`leczcr lucgkd  E 9 1 β 7 9.69 m) Lcblub` `b vcbdr k`b `stckîsthld k` pru`mc.

 

 z >

  9.60∝9.69

∑

( 9.60 )( 9.=0 )

>3.30;6

399

 z >3. 3.: : ;0 l) ´Luãb `s su k`lhshüg r`sp`ltd k` bc ehpüt`shs gubc4

 Gd s` r`leczc E9 y s` ldglbuy`  β ≫ 9.69 ==. \`cg bcs shfuh`gt`s ehpüt`shs1

 E 9 1 β >9.;9  E 3 1 β ≩ 9.;9

Pgc nu`strc k` 3=9 dms`rvclhdg`s r`v`bü qu` p > 9.9.;9

]`leczcr lucgkd  E 9 1 β ≩ 9.;9 m) Lcblub` `b vcbdr k`b `stckîsthld k` pru`mc.

 z >

  9.399 , ό > ;99 , U  v`rhjhqu` u` qu` bc prdmcmhbhkck prdmcmhbhkck k` ldn`t`r ug `rrdr thpd HH s`c k` 9.:6

88==∝8 8 ; 9 ;99

>∝9 . ; 0

∑ 399  ν >3 ∝9. 9.:6 ;0999  E 3 1 β ≩ ;0999

=. Ghv`b k` shfghjhlcglhc 9,90

;0999∝ ;0999 9

∑ 3 = 9

;. Ybcgt`cr bc r`fbc k` k`lhshüg Cl`ptd E9 ]`leczd E9 \h Q 7 3.:;0s` r`leczc bc E 9 y s` cl`ptc bc E3 0. [dncr bc k`lhshüg Ldnd Q(9) 2 3.:;0 gd s` r`leczc E9



09∝ ;5.35

> 3.83

< 39 ∑ 39

t >=.5=3

 Gd s` r`leczc E9 `b p`sd n`khd `s hgj`rhdr c 09 bhmrcs m) Hgkhqu` `g ug mr`v` hgjdrn` bc rczüg pdr bc qu` ]utt`r pu`k` uthbhzcr bc khstrhmulhüg z

ldnd `stckîsthld k` pru`mc. \` ldgdl`g bds `stckîsthlds \hfu` ugc khstrhmulhüg gdrncb l) Lcblub` `b vcbdr p.

 p > 9.93