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Segunda Asignacin de Estadstica Aplicada a la Ingeniera Qumica

CDIGO APELLIDOPATERO

APELLIDO!ATERO

O!"RES Pr#$lema

Pr#$lemas Problema

Asignado

Supp#se t%atf &x' ( )&*x +x, ' - ,./ 0#r 1 2x 2 *3Determine t%e 0#ll#4ing5&a'P&X 2 ,' &$'P&X 2 6' &c'P&, 2X 2 7'&d'P&X 8 /' &e'x suc% t%atP&X 2x' ( 136.

9

A test instrument needs t# $e cali$rated peri#dicall: t# pre;ent measurement ,

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err#rs3 A0ter s#me time #0 use 4it%#ut cali$rati#n< it is =n#4n t%at t%epr#$a$ilit: densit: 0uncti#n #0 t%e measurement err#r isf &x' ( 9+ 13.x 0#r 12x 2 , millimeters3&a' I0 t%e measurement err#r 4it%in 13. millimeters is accepta$le< 4%at is t%epr#$a$ilit: t%at t%e err#r is n#t accepta$le $e0#re cali$rati#n>

&$' ?%at is t%e ;alue #0 measurement err#r e@ceeded 4it% pr#$a$ilit: 13,$e0#re cali$rati#n>&c' ?%at is t%e pr#$a$ilit: t%at t%e measurement err#r is e@actl: 13,,millimeters $e0#re cali$rati#n>i3 T%e pr#$a$ilit: densit: 0uncti#n #0 t%e net 4eig%t in p#unds #0 a

pac=aged c%emical %er$icide isf &x' ( ,31 0#r 763. 2x 2 .13,.p#unds3&a' Determine t%e pr#$a$ilit: t%at a pac=age 4eig%s m#re t%an .1p#unds3&$' B#4 muc% c%emical is c#ntained in 61 #0 all pac=ages>

ii3 T%e li0e #0 a recirculating pump 0#ll#4s a ?ei$ull distri$uti#n 4it%parameters

( , and

( 11 %#urs3 Determine5

&a' !ean li0e #0 a pump &$' ariance #0 t%e li0e #0 a pump&c' ?%at is t%e pr#$a$ilit: t%at a pump 4ill last l#nger t%an its mean>

)

Supp#se t%at t%e cumulati;e distri$uti#n 0uncti#n #0 t%e rand#m ;aria$leXis

F(X)={ 0 x

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#0 /11x+, 0#r 911 Fm 2x 2 9,1 Fm3&a' Determine t%e mean and ;ariance #0 t%e c#ating t%ic=ness3&$' I0 t%e c#ating c#sts 13.1 per micr#meter #0 t%ic=ness #n eac% part< 4%atis t%e a;erage c#st #0 t%e c#ating per part>T%e t%ic=ness #0 p%#t#resist applied t# 4a0ers in semic#nduct#r

manu0acturing at a particular l#cati#n #n t%e 4a0er is uni0#rml: distri$uted$et4een 13,1.1 and 13,9.1 micr#meters3 Determine t%e 0#ll#4ing5&a' Cumulati;e distri$uti#n 0uncti#n #0 p%#t#resist t%ic=ness&$' Pr#p#rti#n #0 4a0ers t%at e@ceeds 13,9,. micr#meters in p%#t#resistt%ic=ness&c' T%ic=ness e@ceeded $: 91 #0 t%e 4a0ers &d' !ean and ;ariance #0p%#t#resist t%ic=ness

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T%e ;#lume #0 a s%amp## 0illed int# a c#ntainer is uni0#rml: distri$uted$et4een )7 and )*1 milliliters3&a' ?%at are t%e mean and standard de;iati#n #0 t%e ;#lume #0 s%amp##>

&$' ?%at is t%e pr#$a$ilit: t%at t%e c#ntainer is 0illed 4it% less t%an t%ead;ertised target #0 ). milliliters>&c' ?%at is t%e ;#lume #0 s%amp## t%at is e@ceeded $: 6. #0 t%ec#ntainers>&d' E;er: milliliter #0 s%amp## c#sts t%e pr#ducer 1311,3 An: s%amp##m#re t%an ). milliliters in t%e c#ntainer is an e@tra c#st t# t%e pr#ducer3?%at is t%e mean e@tra c#st>

6

i3 Assume t%atZ %as a standard n#rmal distri$uti#n3Hse Ta$le t# determine t%e ;alue 0#rz t%at s#l;es eac% #0 t%e 0#ll#4ing5&a'P&Z &$' ?%at is t%e pr#$a$ilit: t%at a sampleJs strengt% is $et4een .*11 and.611 Kgcm,>&c' ?%at strengt% is e@ceeded $: 6. #0 t%e samples>

99

!easurement err#r t%at is n#rmall: distri$uted 4it% a mean #0 1 and astandard de;iati#n #0 13. gram is added t# t%e true 4eig%t #0 a sample3 T%en

9,

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t%e measurement is r#unded t# t%e nearest gram3 Supp#se t%at t%e true4eig%t #0 a sample is 9/.3. grams3&a' ?%at is t%e pr#$a$ilit: t%at t%e r#unded result is 9/ grams>&$' ?%at is t%e pr#$a$ilit: t%at t%e r#unded result is 9/ grams #r m#re>P%#eni@ 4ater is pr#;ided t# appr#@imatel: 937 milli#n pe#ple 4%# are

ser;ed t%r#ug% m#re t%an )/,&$' Appr#@imate t%e pr#$a$ilit: #0 0e4er t%an ).1 err#rs in a m#nt%3&c' Appr#@imate a ;alue s# t%at t%e pr#$a$ilit: t%at t%e num$er #0 err#rse@ceeds t%is ;alue is 131.3&d' Appr#@imate t%e pr#$a$ilit: #0 m#re t%an 711 err#rs per m#nt% in t%e

ne@t t4# m#nt%s3 Assume t%at results $et4een m#nt%s are independent3

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Supp#se t%at t%e num$er #0 as$est#s particles in a sample #0 9 suaredcentimeter #0 dust is a P#iss#n rand#m ;aria$le 4it% a mean #0 91113 ?%atis t%e pr#$a$ilit: t%at 91 suared centimeters #0 dust c#ntains m#re t%an91

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Supp#se t%atX %as an e@p#nential distri$uti#n 4it% ( ,3 Determine t%e0#ll#4ing5&a'P&X M 1' &$'P&X N ,'&c'P&X M 9' &d'P&9< X &$' ?%at is t%e pr#$a$ilit: t%at an assem$l: #perates 0#r m#re t%an .11%#urs $e0#re 0ailure>&c' I0 an assem$l: %as $een #n test 0#r 711 %#urs 4it%#ut a 0ailure< 4%at ist%e pr#$a$ilit: #0 a 0ailure in t%e ne@t 911 %#urs>&d' I0 91 assem$lies are tested< 4%at is t%e pr#$a$ilit: t%at at least #ne 0ailsin less t%an 911 %#urs> Assume t%at t%e assem$lies 0ail independentl:3

&e' I0 91 assem$lies are tested< 4%at is t%e pr#$a$ilit: t%at all %a;e 0ailed $:*11 %#urs> Assume t%at t%e assem$lies 0ail independentl:3

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An article inJournal of Hydrology Hse #0 a L#gn#rmal Distri$uti#n!#del 0#r Estimating S#il ?ater Retenti#n Cur;es 0r#m ParticleSieDistri$uti#n Data &,11/< #l3 ),)&9'< pp3 ),.))7'U c#nsidered al#gn#rmal distri$uti#n m#del t# estimate 4ater retenti#n cur;es 0#r a range#0 s#il te@tures3 T%e particlesie distri$uti#n &in centimeters' 4as m#deledas a l#gn#rmal rand#m ;aria$leX 4it% V ( +)3* and W ( 133 Determine t%e

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0#ll#4ing5&a'P&X 2 131,' &$' alue 0#rx suc% t%atP&X Mx' ( 136.&c' !ean and ;ariance #0X

T%e lengt% #0 an inXecti#nm#lded plastic case t%at %#lds magnetic tape isn#rmall: distri$uted 4it% a lengt% #0 613, millimeters and a standardde;iati#n #0 139 millimeter3&a' ?%at is t%e pr#$a$ilit: t%at a part is l#nger t%an 613) millimeters #rs%#rter t%an *63 millimeters>&$' ?%at s%#uld t%e pr#cess mean $e set at t# #$tain t%e %ig%est num$er #0parts $et4een *63 and 613) millimeters>&c' I0 parts t%at are n#t $et4een *63 and 613) millimeters are scrapped< 4%atis t%e :ield 0#r t%e pr#cess mean t%at :#u selected in part &$'> Assume t%att%e pr#cess is centered s# t%at t%e mean is 61 millimeters and t%e standardde;iati#n is 139 millimeter3 Supp#se t%at 91 cases are measured< and t%e: areassumed t# $e independent3&d' ?%at is t%e pr#$a$ilit: t%at all 91 cases are $et4een *63 and 613)millimeters>

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