8/12/2019 Exam 3 001 a FALL 008 Solutions

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EXAM 3 Version A   (as!" #irs! $ Mi%%&e Ini!ia&'

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8/12/2019 Exam 3 001 a FALL 008 Solutions

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T*e area un"er !*e s!an"ar" normal ur#e +*ere ( - . /01) is:

a 23045 6 7304

0873" 9873

1 T*e area un"er !*e s!an"ar" normal ur#e +*ere (- /81) is:

a ;27; 6 7747 981" 90185

3 T*e pro6a6ili!< !*a! an o6ser#a!ion !a&en from a s!an"ar" normal popula!ion:

( =7 . - . /7):

a ;412 6 09;7 470;5" 2;3;

7 T*e (91 . - . 179)

a 981 6 4013 ;;9" 7045

0 T*e ele!roni "a!a !ransmission lines are sai" !o *a#e a !ransmission ra!e of 1(999,999) 6i!s per seon"> +i!* a s!an"ar" "e#ia!ion of 1 (999,999) 6i!s perseon" an" follo+ a normal "is!ri6u!ion If <ou !es! one of !*e lines, +*a! is !*e pro6a6ili!< of fin"in? a line +i!* a !ransmission ra!e of less !*an 9 (999,999) 6i!s per seon"

a 2887 6 0;45 373" 9;2;

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8 Spiral E#er?lo @ul6s are &no+n !o *a#e a mean of life of 099 *ours an" as!an"ar" "e#ia!ion of 79 *ours *a! peren!a?e of 6ul6s sol" +oul" <ou eBpe!!o las! more !*an 799 *ours

a 88;

 6 0;4 223;5" 7131

4 Ama"eus C*eese is reall< ?oo" an" *ole Foo"s (F) is al+a<s runnin? ou! ofs!o& From !*e "a!a !*e< *a#e olle!e" !*e< sell an a#era?e of 79 poun"s permon!* +i!* a s!an"ar" "e#ia!ion 19 poun"s If F +an!s !o mee! "eman" 20 of!*e !ime, +*a! uan!i!< s*oul" !*e< 6rin? in for !*e mon!*s sales

a 435 6 87

74" 38

; F "ei"e" !o in#es!i?a!e !*eir "a!a an" sample" for 2 mon!*s an" onlu"e"+i!* !*e mean +as reall< 7; poun"s +i!* a *no+n s!%, %eia!ion of 19 T*eanal<s!s *a#e 6een as&e" *o+ onfi"en! !*e< are in !*is es!ima!e of !*e mean> so!*e< es!a6lis*e" a 20 onfi"ene in!er#al (CI) T*e upper limi! of !*is CI is:

a 03 6 04 85" 8;

2 Refer !o 2 a6o#e Gana?emen! "ei"e" !*a! !*e< "i" no! li&e an error of !*ir!een poun"s, so !*e< ame 6a& !o !*e anal<s!s an" as&e" *o+ man< mon!*s !*e<+oul" *a#e !o sample !o ?e! an error of 9 poun"s ( 20 CI) You 6ein? a?rea! *i?*l< pai" anal<s! sai"JJJJJJJJ mon!*s

a 11 6 85 1" 9

9 If !*ere is an ;9 pro6a6ili!< !*a! of - 6ein? 6e!+een $ - an" /- en!ere" a6ou!!*e mean> !*en !*e #alue of - is:

a 1;5 6 71 119" 947

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T*e Gen!orin? %roup ?i#e an eBam !o ma&e sure !*ose +*o appl< are ualifie" as

!u!ors T*e mean sore is ;7 +i!* a s!an"ar" "e#ia!ion of 1 I! is "ei"e" !*a!!*e< +ill aep! for in!er#ie+s !*ose applian!s a6o#e !*e 30 !* peren!ile *a! is!*e u!off sore for aep!ane

a 23 6 ;;7 4235" 414

1 If <ou *a#e a ! "is!ri6u!ion +i!* "f K 2 an" ! K 1;1> +*a! of #alues "o <oueBpe! !o lie a6o#e !*is #alue

a 1; 6 849 ;37" 995

3 For a ! "is!ri6u!ion +i!* 7 "e?rees of free"om an" 29 of !*e area is !o !*e ri?*!of !*e ! #alue> !*e ! #alue is JJJJJJJJJJJJJJ

a =3705 6 =170 /341" /18;

7 %oo" Ar?en!inean Gal6e *as 6eome #er< popular T*e a#era?e prie is299M6o!!le T*e &no+n s!" "e# is 899 *a! is !*e pro6a6ili!< of sele!in? a 6o!!le a! ran"om !*a! *as a prie less !*an 199 (Assume Normal)

a 8205 6 02 31;0" ;1;0

0 %i#en !*e "a!a in ues!ion 7 a6o#e, +*a! is !*e pro6a6ili!< of sele!in? 7 6o!!les !*a! *a#e an aera.e /rie ?rea!er !*an 99 Assume Normal

a 907 6 97441 91075" 92441

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8 199 s!u"en!s !a&e !*e Amerian Soie!< for uali!< SiB Si?ma EBam T*e soresfollo+ a normal "is!ri6u!ion +i!* an a#era?e sore of 40 an" a &no+n s!an"ar""e#ia!ion of 9 *a! is !*e pro6a6ili!< of a s!u"en! sele!e" a! ran"om sorin?more !*an ;9 se !*e - !a6le

a 1973 6 0724 39;05" ;999

4 Garia is ma&in? a mar&e!in? "eision an" sur#e<s nine super mar&e!s an" fin"s!*a! !*e< 6u< an" aera.e o 0 ases of GariaPs Canne" Gaa"amia Nu!s per+ee& T*e &no+n s!an"ar" "e#ia!ion is 9 asesM+ee& Garia *as "ei"e" !*a! if!*e error !erm is more !*an 8 a! !*e 29 onfi"ene le#el s*e +ill "o moresamplin?

a Sample more 6 DonP! sample more5

; sin? !*e "a!a in ues!ion 4 a6o#e, +oul" <our "eision *an?e a! !*e 20onfi"ene le#el> s*oul" <ou sample more or no!

a Sample more5 6 DonP! sample more

2 A fine foo"s s!ore sells #er< ?oo" apers an" is onerne" a6ou! i!s in#en!ories>!*erefore !*e mana?er *as es!ima!e" !*e mean mon!*l< sales uni!s an" 6uil! a 20onfi"ene in!er#al a6ou! !*e mean T*e Lo+er Limi! is 189 uni!s an" !*e pperLimi! is 389 uni!s Assume a normal "is!ri6u!ion T*e mean is

a 819 6 395 1;8" No! enou?* informa!ion !o !ell

19 %ourme! S*a& sells an a#era?e of 00 pa&a?es "ail< of eBellen! En?lis* S!il!onC*eese T*e sales *a#e a s!an"ar" "e#ia!ion of 9 pa&a?es per "a< an" salesfollo+ a normal "is!ri6u!ion If !*e in#en!or< mana?er &eeps 40 pa&a?es on*an", +*a! peren!a?e () of "eman" "o <ou eBpe! !o mee!

  a 40;3  6 ;711  24415  "9999

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1 For a s!an"ar" normal "is!ri6u!ion +*a! is !*e pro6a6ili!< !*a! 9. - .39

a 0475

 6 373 72;4" ;777

11 A ran"om sample of 10 o6ser#a!ions is !a&en on assem6l< !imes for alula!orsan" !*e mean !ime is foun" !o 6e 38 minu!es +i!* a sample s!an"ar" "e#ia!ion of7 minu!es, T*e lo+er 6oun" of a ;9 onfi"ene in!er#al is:

a 3; 6 1229

39005" 171

13 C*oose !*e s!a!emen! !*a! is !rue

a *en usin? a sample s!an"ar" "e#ia!ion, <ou s*oul" use !*e -, S!an"ar" Normal Ta6le, !o ons!ru! a onfi"ene in!er#al for !*e popula!ion mean

 6 T*e +i"er <our onfi"ene in!er#al, !*e more fai!* <ou *a#e in <our poin!es!ima!e of !*e mean

A 29 onfi"ene in!er#al for !*e popula!ion mean +ill 6e more narro+!*an a 20 onfi"ene in!er#al for !*e popula!ion mean5

" If <ou re samplin? for means an" <ou u! !*e sample siQe in *alf, !*es!an"ar" "e#ia!ion of !*e means +ill 6e u! in *alf

17 Assume !*a! a 29 Confi"ene In!er#al on !*e mean is !o 6e ons!ru!e" +i!* amaBimum error E K 8 uni!s T*e popula!ion s!an"ar" "e#ia!ion is 39 *a! is !*eminimum sample siQe reuire" !o mee! !*ese speifia!ions

a 39 6 30 79" 09 +ill 6e plen!<5

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10 If a sample siQe of 99 +as neessar< !o es!ima!e !*e mean of a normal popula!ionof 6a??e" "o? foo" !o +i!*in 1 ounes, +i!* a 20 onfi"ene in!er#al, +*a! is!*e #alue of !*e s!an"ar" "e#ia!ion

a 7

 6 01 499" 815

18 T*e mean life of a !ele#ision 19 mon!*s +i!* a #ariane of 28 mon!*s If asample of 87 !ele#isions is sele!e" ran"oml<, +*a! is !*e pro6a6ili!< !*a! !*esample mean +oul" "iffer from !*e !rue mean 6< less !*an 0 mon!*s 

a 97242 6 9220;5

9991" 99971