Ejercicios 31 a 64.docx
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31)
σ
σ
2
2
[ M −Z
∗σ
√ n
; M + Z
∗ σ
❑
]
(6.5-(1.96*1.7); (6.5-(1.96*1.7); 6.5+(1.96* 1.7) -3.168 ; 9.832
32) N=(X-
Z
σ
¿
2
σ
√ n
;
Z
X+
σ 2
¿
σ
√ n )
N= 3-1.96*0.03/36 ; 3+1.96 * 0.03/36) -2.99 ; 3.0098
33) N=(X-
Z
σ
¿
2
σ
√ n
;
X+
Z
σ 2
¿
σ
√ n )
N= (50-2.575* 0.03/0.29; 50+2.575 * 0.03./2.029) -49.94 ; 50.11
34) ) N=(X-
Z
σ 2
¿
σ
√ n
;
Z
X+
σ 2
N=(50-(.96*6.2/ 26; 50+1.96*6.2/26) -47.61 ; 52.38
35) )
[ M −Z
σ
σ
2
2
∗ σ
√ n
; M + Z
∗ σ
❑
]
(40-1.645 * 3.07; 40+1.645*3.07) 34.94 ; 45.05
¿
σ
√ n )
36)
[ M −Z
σ
σ
2
2
∗σ ; M + Z
√ n
∗ σ ]
❑
(60-(2.17*0.75) ; 60+ (2.17*0.75) -58.37 ; 61.627
37)
[ M −Z
σ
σ
2
2
∗σ
√ n
; M + Z
∗σ
❑ ]
0.99 + 0.005=0.995 0.995-0.50=0.495 =2.58 8.2/50= 1.16 (70-2.58*1.16;70+2.58*1.16) -67.007 ; 72.99 σ
38) M − Z
2
σ
∗σ
√ n
; M + Z
2
∗σ
❑
¿
(1820-(1.96*98.38) ; 1820+(.96*98.38) -1627; 2012.82
39) (50+( 1.96*2.92); 50+(1.96*2.92) (44.28 ; 55.72) 40) (290+(1.96*27.95) ; 290 + (1.96*27.95) (235.22 ; 344.78) 41) (14.38 + (1.29 *18.92) ; 14.38 + (1.29*1892) (16821.68 ; 11940.32)
42) 0.98 + 0.01 = 0.99 0.99 -0.50 = 0.4901 = 2.33 (24-(2.33 *1.29) ; 24+(2.33*1.29) (27.006 ; 20.99) 43) 0.90+0.05 =0.95 0.95 – 0.5 =0.45= .65 (60-(1.65*12) ; 60 + (1.65*12) (79.80 ; 40.20)
EJERCICIO # 51 Ed!"d $%&$' d %! ,%$! d R$" C$ $'"! 500 $'"!$' d "'$ % ,!!d. :'! "! d 35 d ! $'"!$' " %! ! d$! d %! %! d ! d 99? d %! ,","$' d %$' ' '! d $'' '! !"! F$! ' % !'. N = 650 @ = 50 A$!$' = 26 C'!'>! = 99? B"%!
σ
σ
2
2
[ M −Z
(
[50 −
∗ σ
√ n
2.575
; M + Z
∗26
√ 650
∗σ
√ n
) ( ; 50 +
]
2.575
)
∗26 ]
√ 650
[ 47.37 ; 52.62 ] R// E% $'"!% d '!'>! !% ' % "!' d 47.37 52.62
D, ' %! !,!'! d !.
EJERCICIO # 53 G $! 60? d % !" d E!d :'$d '"!! %$$' ," !%. H d !"! "$!" ! !"!$' ,!"! %! d '$!$' !$!. G$ d! $!d" ''" ! ' d 5 ,' ,"'!% ' ' '$% d '!'>! d 95? !!K d "! "$"L '= M>! !%! d$ * A$!$' ,$! / EP '= M 1.96*5/5P '= 3841.6
EJERCICIO # 54 :d '$! !%%!" %! !'$d!d d$! d d! $!!' !% !K % 'dd". Q! d$! d ' ,K d$ ,$% d 150 d! ' '! d$!$' 'd!" d 14 d!. G$ d d !%%!" %! d$! ,%!$'!% ! ' d 2 d!. ! ' 'dd" d $'%$" ' %! "!L :$%$ ' $'"!% d '!'>! ," 90 ," $'. @ = 150 A$!$' = 14 C'!'>! = 90?
n
=(
∗
1.645 14 2
2
)
n =132.60
R// G d $'%$" ! 133 'dd".
EJERCICIO # 55 :d ! ! %%!" ! ! % 'd d '! "! ,!"! d"$'!" % $'" d$ !$%$!" ' ' "! ""!% d% '" d B%"$d!. Q! ,"'! ! '! !$%$! d $'%$" ' %! "!L E' '! "! ,$% d 10 !$%$! %! d$!$' 'd!" d %! "! d ! = 95? n =(
∗
1.96 500 100
2
)
n =96.04
R// G d" '"$!" ! 96 !$%$!.
EJERCICIO # 56 B!$%$ :GH "$! '!% "!! d ! "%!$'!d ' %! !%d ' ! 20 d "$,". E''" %! ,"$! !'!% d " d !%d ,!"! '! !$%$! ' ""! d '! ,"! ,"d$!"' ! ' $'"!% d '!'>! d 99? ,!"! %! ,"$' $!%' d %! d$! ,%!$'!%. ) A !!K '$! " %! "! ,!"! %! d$! d %! ,%!$' ''" d'" d ' !"' d 25 ,$ ' '! '!'>! d 95 ," $'L N = 30 @ = 8000
A$!$' = 300 C'!'>! = 95? a)
(
[ 8000−
2.575∗300
√ 30
)
; 8000 +
(
2.575∗300
√ 30
)
]
[7858.96 ; 8141.04 ] R // E% $'"!% d '!'>! !% ' % "!' d 7858.96 8141.04
D, ' %! !,!'! d !. b)
(
1.96
∗300
25
2
)
M553.19P R // Q! "! d" "",'d" ! 553
58 :'! "! !%!"$! d 25 ,"'! ,%!d! ," %! !"$d!d d% !d d T"$d! !%$ !'!!' ' !%!"$ ,"d$ (' ,"!$') d ! d 99? d% !%!"$ d$ d %! ,%!$' (' ,"!$') d ,%!d
0.005 61.78
0.005 68.21 0.99 0.995 65
1-0.99= 0.01/2=0.005 2.57+2.58/2 = 2.575 M65-2.575*6.25/S25 ; 65+2.575*6.25/S25P M61.78; 68.21P ) d !!K d " %! "! ,!"! !%%!" %! d$! d %! ,%!$' ' ' """ !d$$% d ! d 95? N = (1.96* 6.25)/1.00 = 150.06
59.
:'! !%$!'>! $'!"! $%$> '! "! !%!"$! d 50 $d!d!' !d'$d' ,!"! !%%!" % !d'$d' U' $ $d ,%%! ' AFA 78 "! % !K ,!!d. Q! d$!$' 'd!" d ! "! d 9 "! !) C'"! % $'"!% d '!'>! d 95? d %! !'$d!d d$! ,%!$'!% d "! ,%!d! ' " $d ,%%! ' AFA % !K ,!!d
0.025 75.50
0.025 80.49 78 0.95
0.975
1-0.95= 0.05/2 0.025 0.975= 1.96 M78-1.96*9/S50 ; 78+1.96*9/S50P M 75.50 ; 80.49P ) A !!K d " %! "! ,!"! "% 90? '!% d %! d$! d %! "! ''"! d'" d ' !"' d 1.0 "! d %! d$! ,%!$'!%.
0.05
0.05
0.90 0.95
0.95 ' V = 1.64+1.65/2= 1.645 N = (1.645* 9)/1.00 = 219.18
60
A%!' ' %%! "$" $% d %! $'$! ' % ! d $% d ' !. A, d %! ,"$"! ' %%' % !' ''" %! d$! "! d 23.4 $%%! ," !%' (,) ' '! d$!$' 'd!" "!% d 0.9 @W !) C!%% % $'"!% d '!'>! d% 95? ,!"! ,
0.025
0.025
22.81
23.988
23.4 0.95 0.975 1-0.95= 0.05/2= 0.025 0.975 ' V =1.96 M23.4-1.96*0.9/S9 ; 23.4+1.96*0.9/S9P M22.81; 23.988P ) C!'! d %%'!" % !' d !%$'! ,!"! '" ' !"' d """ ," d! d 0.1@, E = V!%!/2*A$!$'/S' '= MA$!$' (V!%!/2)/E)P 2 '= M0.9(1.96)/0.1P 2 = 231.3
61
E' '! '! ! 36 ,",$!"$ d I,' %$'!d !% !>!" " % ,"$ d ,"! $' '! d$! d ! d 95? d %! d$!
0.025 474.8
0.025 357.2 416 0.95 0.975 1-0.95= 0.05/2= 0.025 0.975 ' V = 1.96 M416-1.96*180/S36 ; 416+1.96*180/S36 P M357.2 ; 474.8P
) A !!K d " %! !% ,!"! $!" %! d$! ,%!$'!% d'" d 10 N = (1.96*180)/10 = 35.28 62 :d ,%!'! %%!" ! ! '! '! ,!"! !%%!" %! ,","$' d ">! %!"!% ' d "!!. A$d ' ! ' ' '$% d '!'>! d 95? !% %! ,","$' $!d! d ''"!" ' ' !"' d ' 2? d %! ,","$' ,%!$'!%. :'! '! ,$% "%! 5 d 50 d % '"$!d '! d "!!. ! ' "!!!d" d '"$!" ,!"! !$!" % "$$. R// 5/300*100 = 1.66
63 Q! ,","$' d '!d" ,U%$ !$!"' d ,"! ' % U%$ " !K d! !%%!" ' ' !"' d 3?. E '!"$ $%$>!" % '$% d '!'>! d 95?. :' d$ "!%$> ! !"$ !K "% % ,"'! d '!d" ,U%$ !$ d ,!K! ' " !K d 21 H) W!"! !!%$>!" % d$ C% % 'U" d D,d$' d '!d" ,U%$ d' d$!"L 21/700= 0.03*100 =3? ) ' ' '!d" ,U%$ '!"$ ,'" ' '! $ ' '! ' $!d" !'"$" d %! ,","$' ,%!$'!% H% ' 750 64 C ,!" d '! "$$' !'!% d '! ' ""d" %$'! '! "! !%!"$! d 36 %$'. H% "$!" '! !%% '! d$! d
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