Trabajo Colaborativo Fase2
Short Description
Descripción: Trabajo Colaborativo Fase2...
Description
UNIDAD 2 FASE 2
PRESENTADO POR:
PRESENTADO A:
GRUPO: 100402_322
UNIVERSIDAD NACIONAL ABIERTA Y A DISTANCIA – UNAD VISUAL BASIC B ASIC AVANZADO AVANZADO 2016
Introducción
El siguie!e !"#$#%& '&!iee el (es#""&ll& (e l&s ) '#s&s *"&*ues!&s *#"# l# '&+* '&+*"e "esi si, , (e l# ui( ui(#( #( 2 (el (el 'u"s& 'u"s& (e *"&$ *"&$#$ #$ilili( i(#(#(- el 'u#l 'u#l se #(.ui #(.uie" e"e e (es!"e/#s e el (es#""&ll& #(e'u#(& (e *"&$le+#s u!ili/#(& l&s '&&'i+ie!&s #(.ui"i(&s (u"#!e el es!u(i& (el 'u"s&
Objetivo Genera
Des#""&ll#" ) '#s&s *"&*ues!&s e l# gu# i!eg"#(&"# (e #'!ii(#(es u!ili/#(& l&s '&&'i+ie!&s #(.ui"i(&s e el es!u(i& (e l# ui(#( 2
Objetivo! e!"ec#$ico!%
•
•
• •
I(e!i I(e!i3i' 3i'#" #" l&s !4"+i !4"+i&s &s (e l# 3u'i, 3u'i, (e *"&$#$ *"&$#$ili ili(#((#(- #l&" es*e"#( es*e"#(&&#"i#/# 5 (esi#'i, es!(#" Re#li/#" el (es#""&ll& (e ) '#s&s e3e'!u#(& l&s *#s&s #(.ui"i(&s e l# ui(#( 2 Re#li/#" #*&"!es (el '#s& es'&gi(& *#"# el (es#""&ll& (e l# #'!ii(#( g"u*#l Re#li/#" el '&s&li(#(& (el !"#$#%& 3i#l 5 *&s!e"i&" *"ese!#'i,
ANE&O 2 ES'UDIOS DE (ASO ES'UDIO DE (ASO 1
1
P#"# e!"eg#" u# T#"%e!# (e '"4(i!& e l&s $#'&s (el g"u*& A#l- l&s ##lis!#s (el $#'& 'l#si3i'# & '#li3i'# #l 'lie!e e 3u'i, (e l# *"&$#$ili(#( (e .ue "esul!e "e!#$le U# !#$l# 7#$i!u#l (e '#li3i'#'i&es es l# siguie!e:
1
L# '#li3i'#'i, es l# su+# (e l&s *u!&s (e l&s seis "u$"&s P&" e%e+*l&Sus7i B"&8 !iee +e&s (e 2) #9&s 12 *u!&s;< 7# ii(& e el +is+& (&+i'ili& (u"#!e (&s #9&s 0 *u!&s;< (es(e 7#'e 'u#!"& #9&s es (ue9& (e u #u!&+,il 1= *u!&s;- *&" el .ue "e#li/# *#g&s (e >?) 6 *u!&s;< "e#li/# g#s!&s (&+4s!i'&s (e >200 10 *u!&s; 5 *&see u# 'ue!# (e '7e.ues = *u!&s; L# '#li3i'#'i, .ue &$!e("# se"# (e @@ Des*u4s- '& u# segu(# !#$l#- se '&ie"!e l#s '#li3i'#'i&es e *"&$#$ili(#(es (e "e!#$ili(#( (el 'lie!e- #s:
L# *u!u#'i, (e Sus7i @@; se !"#(u'i"# e u# *"&$#$ili(#( (e "e!#$ili(#( #*"&i+#(# (e 01 E &!"#s *#l#$"#s- 1 (e l&s 'lie!es '&+& Sus7i gee"#"# (ie"& # l#s &*e"#'i&es '& !#"%e!# (el $#'& A '&!iu#'i,- se +ues!"# l&s "esul!#(&s (e l#s e!"eis!#s '& l&s !"es *&si$les 'lie!es
P"e*#"e u i3&"+e e el .ue '&+& +i+&- i'lu5#:
1 C#li3i.ue # '#(# u& (e es!&s 'lie!es 5 '#l'ule l# *"&$#$ili(#( (e .ue "esul!e "e!#$les
No)bre
Eda d
'ie)"o Anti*+eda de vivir d con e en a auto )i!)a re!idenci a
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(o!to de viviend a
(uenta 'ota de c-e.ue ! o a-orro!
D#i( B"&8
1
20
1=
@
10
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/0
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12
0
1=
6
10
=
44
A 'l#ug7li
0
20
=
@
12
0
3
F#ll#+&s l# "el#'i, e!"e el !#+#9& (e l&s i!e"#l&s 10 *u!&s; '& l# (i3e"e'i# .ue se *"ese!# (e l# *"&$#$ili(#(
N&+$"e
C#li3i'#'i,
P"&$#$ili(#(
D#i( B"&8
0
0)
E(8#"( B"e(#
@@
01
A 'l#ug7li
=
0??
2 HCul es l# *"&$#$ili(#( (e .ue l&s !"es "esul!e "e!#$les
L# *"&$#$ili(#( (e .ue l&s !"es "esul!e "e!#$les se (e!e"+i# *&" l# *"&$#$ili(#( '&(i'i&#l *#"# es!e '#s& (&(e l&s su'es&s '& & i'lu5e!es P ( A )∗ P ( B )∗ P ( C ) 0.95∗0.81∗0.77 =0.59
= HCul es l# *"&$#$ili(#( (e .ue igu& se# "e!#$le L# *"&$#$ili(#( (e .ue igu& se# "e!#$le- se (e!e"+i# *&" l# *"&$#$ili(#( '&(i'i&#l *#"# 'u#(& & se# "e!#$le- .ue es l# (i3e"e'i# e!"e 1 5 l# *"&$#$ili(#( (e .ue se# "e!#$les
P (− A )=1−0.95 =0.05
P (−B )=1 −0.81=0.19 P (−C )=1− 0.77= 0.23
Se *ue(e '#l'ul#" l# *"&$#$ili(#( '&(i'i&#l
0.05∗0.19∗0.23 =0.0022
@ De!e"+ie l# (is!"i$u'i, (e *"&$#$ili(#( !&!#l (el J+e"& (e 'lie!es "e!#$les e!"e es!e g"u*& (e !"es 'lie!es
De!e"+i#+&s l# (is!"i$u'i, (e *"&$#$ili(#( !&!#l- '&+& u# 3u'i, (e *"&$#$ili(#(
K *u!u#'i, &$!ei(# K1 *u!u#'i, i+e(i#!#+e!e #!e"i&" # K (e l&s #l&"es "el#'i&#(&s e l# !#$l#
P1 P"&$#$ili(#( '&""es*&(ie!e *u!u#'i, #!e"i&" # K (e l&s #l&"es "el#'i&#(&s e l# !#$l#
P ( X = x )=
x − x n−1∗ p− p n−1 10
+ pn−1
) Re(#'!e u $"ee "esu+e (e sus 7#ll#/g&s
E '#s& &s *"ese!# l# *"&$#$ili(#( *#"# su'es&s & e'lu5e!es- l& 'u#l l# su+# (e l# *"&$#$ili(#( & (e$e se" igu#l # 1- (e igu#l +#e"# *&" l# '#"#'!e"s!i'# (e su'es& & e'lu5e!e se *ue(e 7#ll#" l# *"&$#$ili(#( .ue l&s !"es "e!#$les '#l'ul#(& su *"&$#$ili(#( '&(i'i&#l- *#"# '#s& .ue igu& se# "e!#$le se #*li'# l# *"&$#$ili(#( '&(i'i&#l # l#s (i3e"e'i#s e!"e 1- el #l&" (e l# *"&$#$ili(#( (e .ue se# "e!#$les U!ili/#+&s l# 3u'i, .ue "el#'i&# l&s !#+#9&s (e l&s i!e"#l&s (e *u!u#'i, *#"# (es'"i$i" l# (is!"i$u'i, (e l# *"&$#$ili(#(
ES'UDIO DE (ASO 2 2
L# (is!"i$u'i, (e *"&$#$ili(#( $i&+i#l es u# (is!"i$u'i, (e *"&$#$ili(#( (is'"e!# .ue se *"ese!# '& +u'7# 3"e'ue'i# U# (e sus '#"#'!e"s!i'#s '&sis!e e .ue s,l& 7#5 (&s *&si$les "esul!#(&s e u (e!e"+i#(& es#5& (el e*e"i+e!& 5 l&s "esul!#(&s s& +u!u#+e!e e'lu5e!es< O!"# '#"#'!e"s!i'# (e l# (is!"i$u'i, $i&+i#l es el 7e'7& (e .ue l# #"i#$le #le#!&"i# es el "esul!#(& (e '&!e&s Es (e'i"- se 'ue!# el J+e"& (e 4i!&s e el J+e"& !&!#l (e es#5&s U# !e"'e"# '#"#'!e"s!i'# (e u# (is!"i$u'i,
2
$i&+i#l '&sis!e e .ue l# *"&$#$ili(#( (e 4i!& es l# +is+# (e u es#5& # &!"&
U es!u(i& (el De*#"!#+e!& (e T"#s*&"!e (e Illi&is '&'lu5, .ue ?62 (e .uiees &'u*#$# l&s #sie!&s (el#!e"&s (e l&s e7'ul&s u!ili/#$# 'i!u", (e segu"i(#( Es!& sigi3i'# .ue l&s (&s &'u*#!es (e l# *#"!e (el#!e"# u!ili/#$# 'i!u"&es (e segu"i(#( Su*&g# .ue (e'i(e '&+*#"#" l# i3&"+#'i, '& el us& #'!u#l .ue se (# #l 'i!u", (e segu"i(#(- *#"# l& 'u#l sele''i&# u# +ues!"# (e 12 e7'ul&s
P"ese!e u i3&"+e e el .ue '&+& +i+& i'lu5#:
1 HEs!# si!u#'i, 'u+*le '& l&s su*ues!&s (e l# (is!"i$u'i, $i&+i#l I(e!i3.uel&s
F#5 *&si$ili(#(es (e .ue e u e7'ul& e *#"!i'ul#" l&s &'u*#!es (e #(el#!e u!ili'e s & & el 'i!u", (e segu"i(#(
L# *"&$#$ili(#( .ue l&s &'u*#!es u!ili'e el 'i!u", es l# +is+# *#"# 'u#l.uie" e7'ul& el 'u#l '&""es*&(e #l ?62
F#5 u# '#!i(#( 3i%# (e 12 *"ue$#s- *&".ue se e"i3i'# 12 e7'ul&s El "esul!#(& (e u e7'ul& & i3lu5e e &s (e+s 5# .ue l#s *"ue$#s '& i(e*e(ie!es
2 El#$&"e u (i#g"#+# (e $#""#s *#"# l# (is!"i$u'i, (e *"&$#$ili(#( $i&+i#l .ue "e*"ese!# es!# si!u#'i, 0.3
1
2
3
4
5
6
7
8
9
10
11
12
0.25
0.2
P(x)
0.15
0.1
0.05
0 1
2
3
4
5
6
7
8
9
10
11
12
vehiculos
= HCul es l# *"&$#$ili(#( (e .ue l&s &'u*#!es (e l# *#"!e (el#!e"# e e#'!#+e!e ? (e l&s 12 e7'ul&s sele''i&#(&s u!ili'e 'i!u"&es (e segu"i(#(
n =12
π =0.762 n− x
P ( x )=C π ( 1− π ) x
12 − 7
P ( x = 7 )=C ∗0.762 ( 1 −0.762 ) 7
P ( x = 7 )=792 (0.14917 )( 0.00076) P ( x = 7 )=0.0902
@ HCul es l# *"&$#$ili(#( (e .ue l&s &'u*#!es (e l# *#"!e (el#!e"# (e *&" l& +e&s ? (e l&s 12 e7'ul&s u!ili'e 'i!u", (e segu"i(#(
P ( x ≥ 7 )= P ( x =7 ) + P ( x =8 ) + P ( x =9 )+ P ( x = 10 ) + P ( x = 11) + P ( x =12 ) P ( x ≥ 7 )=0.0902 + 0.1805 + 0.2569 + 0.2467 + 0.1436 + 0.0383 P ( x ≥ 7 )=0.9562
) HCul es l# *"&$#$ili(#( (e .ue l&s &'u*#!es (e l# *#"!e (el#!e"# (e +i+& ? (e l&s 12 e7'ul&s u!ili'e 'i!u", (e segu"i(#(
P ( x ≤ 7 )= P ( x =0 ) + P ( x =1 ) + P ( x =2 )+ P ( x = 3 )+ P ( x = 4 ) + P ( x =5 ) + P ( x =6 ) + P ( x =7 ) −8
P ( x ≤ 7 )=3.3∗10
+ 1.27∗10−6 + 2.2∗10−5 + 0.00024 + 0.0017 + 0.0088 + 0.0329 + 0.0902
P ( x ≤ 7 )=0.13386
6 E'ue!"e el #l&" es*e"#(& (el J+e"& (e e7'ul&s e l&s .ue l&s &'u*#!es (e l# *#"!e (el#!e"# u!ili/# el 'i!u", (e segu"i(#(
l# *"&$#$ili(#( .ue se !iee es .ue *#se e7'ul&s '& el 'i!u", (e segu"i(#(
ES'UDIO DE (ASO 3 3
El B#l&!&- es l# l&!e"# e le# (e C&l&+$i#su*e"is#(& *&" ETESA E+*"es# !e""i!&"i#l *#"# l# s#lu(; Es u %ueg& .ue '&sis!e e #'e"!#" 6- )- @ & = J+e"&s e 'u#l.uie" &"(e (e u# +#!"i/ (el 1 #l @)< El %ug#(&" se9#l# e u !#"%e!, l&s 6 J+e"&s .ue es'&ge L&s J+e"&s es! "e*"ese!#(&s e @) $#l&!#s u+e"#(#s (el 1 #l @) C#(# J+e"& #*#"e'e u# s&l# e/ 5 l#s $#l&!#s g##(&"#s se sele''i&# si "ee+*l#/& El *"e+i& #'u+ul#(& se e!"eg# # .uie 7#g# '&i'i(i" l&s seis J+e"&s 3
P"ese!e u i3&"+e e el .ue '&+& +i+& i'lu5#:
1 HEs!# si!u#'i, 'u+*le '& l&s su*ues!&s (e l# (is!"i$u'i, Fi*e"ge&+4!"i'# I(e!i3.uel&s Suge"e'i#: Dii(# l&s @) J+e"&s e (&s g"u*&s: g##(&"es 5 & g##(&"es;
L# (is!"i$u'i, 7i*e"ge&+4!"i'# es es*e'i#l+e!e J!il e !&(&s #.uell&s '#s&s e l&s .ue se e!"#ig# +ues!"#s & se "e#li/# e*e"ie'i#s "e*e!i(#s si (e&lu'i, (el ele+e!& e!"#(& & si "e!&"#" # l# si!u#'i, e*e"i+e!#l ii'i#l
El *"&'es& '&s!# (e *"ue$#s- se*#"#(#s & se*#"#$les (e e!"e u '&%u!& (e N *"ue$#s *&si$les
L# *&$l#'i, N s& l&s @) J+e"&s
L&s ele+e!&s .ue 'u+*le l# *"&*ie(#( s& l&s 6 .ue 7# s#li(& e el s&"!e&
L# +ues!"# .ue !&+#+&s es u# +ues!"# (e 6 J+e"&s
Y l# *"&$#$ili(#( .ue &s (# l# (is!"i$u'i, 7i*e"ge&+4!"i'# es l# (e !ee" (e 0 # seis g##(&"es e l# +ues!"#
2 Us#(& l# (is!"i$u'i, (e *"&$#$ili(#( Fi*e"ge&+4!"i'# (e!e"+i#" l# *"&$#$ili(#( (e .ue el %ug#(&" #'ie"!e l&s 6 J+e"&s
*"&$#$ili(#( (#(# segJ l# 3,"+ul#:
∗( − ) ( ) − ( )= ()
P x
d x
N d n x
N n
M,"+ul# *#"# l&s 6 #'ie"!&s:
P (6 )=
¿
¿
( )( ) = ( ) = ( ) ( )
39 !∗6 ! 45 !
45 −6 6 −6
6 6
45 6
=
1 8145060
1∗
39 0
45 6
1
=¿
45 ! 39 ! −6 !
6! 45∗44∗43∗42∗41∗40
=
720 5864443200
=¿
=1.22773804 ∗10−7 =0.000000122773804
P (6 )=0.000000122773804
= L# e+*"es# e'#"g#(# (el s&"!e& i3&"+# .ue l# *"&$#$ili(#( (e .ue '&i'i(# !&(&s l&s J+e"&s es (e 1 e 1@)060 Hu4 sigi3i'# es!& e !4"+i&s (e *"&$#$ili(#( C&i'i(e es!& '& su "es*ues!# #!e"i&"
De #'ue"(& #l '#s& (e *"&$#$ili(#(
P ( 6 )=1 / 8145060 =1.22773804 · 10
(−7)
L# *"&$#$ili(#( *#"# .ue e u s&"!e& 7#ig# u g##(&" es (e:
(−7)
1.22773804 · 10
El s&"!e& !#+$i4 &!&"g# u *"e+i& si el %ug#(&" 7#'e '&i'i(i" =- @ & ) (e l&s J+e"&s g##(&"es
@; C#l'ule l# *"&$#$ili(#(- *#"# 7#'e" '&i'i(i" = (e l&s 6 J+e"&s g##(&"es
Se u!ili/#" l# 3,"+ul# .ue u!ili/#+&s e el #!e"i&" *u!& '& l&s = #'ie"!&s:
x =3
∗( − ) ( ) − ( )= () d x
P x
N d n x
N n
∗( ) ( ) ( )= = ( )
P x
6 6
39 3
45 3
9.139 14.190
=0,64
); C#l'ule l# *"&$#$ili(#( (e .ue '&i'i(# @ (e l&s 6 J+e"&s g##(&"es
Se u!ili/#" l# 3,"+ul# .ue u!ili/#+&s e el #!e"i&" *u!& '& l&s = #'ie"!&s: x =4
∗( − ) ( ) − ( )= ()
P x
d x
N d n x
N n
∗( ) ( ) ( )= = ( )
P x
6 6
39 2
45 4
741 148995
=0,00497
6; C#l'ule l# *"&$#$ili(#( (e .ue '&i'i(# ) (e l&s 6 J+e"&s g##(&"es
P ( x )=
()( ) () d x
∗ N −d n − x N n
∗( ) ( ) ( )= = ( )
P x
6 6
39 1
45 5
39 1221759
=0,000319
?; HC& $#se e l&s "esul!#(&s &$!ei(&s- us!e( ie"!i"# (ie"& e el BALOTO
C& $#se # l&s "esul!#(&s se ei(e'i# .ue #'e"!#" l&s 6 J+e"&s es '#si i+*&si$le< #'e"!#" l&s ) J+e"&s +e(& i+*&si$le- igu#l+e!e *#"# l&s J+e"&s (el s&"!e& @ 5 =
P&" &!"& l#(&- es 'ues!i, (e sue"!e 5# .ue *ue(e *#s#" +u'7& !ie+*& & u'# *#"# g##"se #lgJ *"e+i& (el $#l&!&
ES'UDIO DE (ASO 4 4
L# (is!"i$u'i, (e *"&$#$ili(#( (e P&iss& (es'"i$e el J+e"& (e e'es .ue se *"ese!# u ee!& (u"#!e u i!e"#l& es*e'3i'& El i!e"#l& *ue(e se" (e !ie+*&- (is!#'i#- "e# & &lu+e L# (is!"i$u'i, se $#s# e (&s su*ues!&s El *"i+e"& '&sis!e e .ue l# *"&$#$ili(#( es *"&*&"'i&#l # l# l&gi!u( (el i!e"#l& El segu(& su*ues!& '&sis!e e .ue l&s i!e"#l&s s& i(e*e(ie!es E &!"#s *#l#$"#s- 'u#!& +s g"#(e se# el i!e"#l&+#5&" se" l# *"&$#$ili(#(< #(e+s- el J+e"& (e e'es .ue se *"ese!# u ee!& e u i!e"#l& & i3lu5e e l&s (e+s i!e"#l&s 4
Es!# (is!"i$u'i, *&see (ie"s#s #*li'#'i&es Se le u!ili/# '&+& +&(el& *#"# (es'"i$i" l# (is!"i$u'i, (e e""&"es e u# e!"#(# (e (#!&s- el J+e"& (e "#5&es 5 &!"#s i+*e"3e''i&es e l#s '#$i#s (e #u!&+,iles "e'i4 *i!#(&s- el J+e"& (e *#"!es (e3e'!u&s#s e e&s- el J+e"& (e 'lie!es .ue es*e"# +es# e u "es!#u"#!e- el J+e"& (e #''i(e!es e u# '#""e!e"# e u *e"i&(& (e!e"+i#(& L# '&+*#9# (e #i#'i, Del!# Ai"lies- se '#"#'!e"i/# *&" su "es*&s#$ili(#( 5 'ui(#(& '& el e.ui*#%e (e sus *#s#%e"&s- *&" l& .ue *&'#s e'es se *ie"(e e.ui*#%e E l# +#5&"# (e l&s uel&s & se *ie"(e +#le!#s< e #lgu&s se *ie"(e u#< e u&s 'u#!&s se *ie"(e (&s< *&'#s e'es se *ie"(e !"es- e!' Su*&g# .ue u# +ues!"# #le#!&"i# (e 1 000 uel&s #""&%# u !&!#l (e =00 +#le!#s *e"(i(#s De es!# +#e"#- el J+e"& *"&+e(i& (e +#le!#s *e"(i(#s *&" uel& es (e 0= P"e*#"e u i3&"+e e el .ue '&+& +i+&- i'lu5#:
1 HEs!# si!u#'i, 'u+*le '& l&s su*ues!&s (e l# (is!"i$u'i, P&iss& I(e!i3.uel&s
Si el u+e"& *"&+e(i& (e +#le!#s *e"(i(#s *&" uel& es (e 0=:
•
L# *"&$#$ili(#( (e .ue & se *ie"(# igu# +#le!# es (e ?@
•
L# *"&$#$ili(#( (e .ue se *ie"(# u# +#le!# es (e 02222
•
L# *"&$#$ili(#( (e .ue se *ie"(# 2 +#le!#s es (e 00===
•
L# *"&$#$ili(#( (e .ue se *ie"(# @ +#le!#s es (e 0000=
2 De!e"+ie 'ul es l# *"&$#$ili(#( (e .ue e u uel& & se *ie"(# igu# +#le!#
0
− 0.3
0.3 ¿ ( e
¿ ¿ p ( 0 ) =¿
)
L# *"&$#$ili(#( (e .ue e u uel& & se *ie"(# igu# +#le!# es (e: 0?@00 ?@;
= De!e"+ie 'ul es l# *"&$#$ili(#( (e .ue e u uel& se *ie"(# e#'!#+e!e u# +#le!#
1
−0.3
0.3 ¿ ( e
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ES'UDIO DE (ASO
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E!"e l#s *e"s&#s si 7&g#"- l# *u!u#'i, +e(i# (el 'ues!i&#"i& CESD es 2=-) '& u# (esi#'i, es!(#" (e ?) 5 se '&si(e"# .ue *#"# l# V#"i#$le K *u!u#'i, (el CESD- a di!tribución e! nor)a% C&+& !"#$#%#(&" e el "e# (e #(+isi&es e u "e3ugi& *#"# *e"s&#s si 7&g#"- us!e( es el e'#"g#(& (e #*li'#" el CESD 5 (e$e e#lu#" l&s "esul!#(&s *#"# l#s ue#s *e"s&#s .ue llegue #l 'e!"&
De!"& (e l#s *&l!i'#s (el "e3ugi& se e'ue!"# .ue 'u#l.uie" *e"s&# 'u5# *u!u#'i, se# (e 20 & +s *u!&s e el CESD (e$e ei#"se # e" # u (&'!&"
INFOE A ,ESEN'A
P"e*#"e u i3&"+e e el .ue '&+& +i+&- i'lu5#:
5
1 L# *"&$#$ili(#( (e .ue u# *e"s&# .ue llegue #l "e3ugi& se# ei#(# # e" #l (&'!&"
desviacionestandar : σ =7,5
mediana y moda por distribuconnormal: µ= 23,5 x =≥ 20
z =
X − µ σ
=
20 −23.5 7,5
=−0.46
P"&$#$ili(#( s&li'i!#(# P [ X ≥ 20 ] =0.1772 + 0.5 =0.6772 L# *"&$#$ili(#( (e .ue u# *e"s&# .ue llegue #l "e3ugi& 5 se# ei#(& # e" #l (&'!&" es 6??2
2 L# *"&$#$ili(#( (e .ue u# *e"s&# .ue llegue #l "e3ugi& !eg# u# *u!#'i, (e 10 & +e&s *u!&s
Se !iee .ue P [ X ! 10 ] =
=
X − µ σ
20 −23.5 7,5
=−1.8
P"&$#$ili(#( s&li'i!#(# P [ X ≥ 10 ] =0.5 −0.4641= 0.0359
L# *"&$#$ili(#( (e .ue u# *e"s&# .ue llegue #l "e3ugi& !eg# u# *u!#'i, (e 10 & +e&s *u!&s es =)
= L# *"&$#$ili(#( (e .ue u# *e"s&# .ue llegue #l "e3ugi& !eg# u# *u!u#'i, e!"e 16 5 20 *u!&s
Se !iee .ue P [ X 20 " y X ≥ 16 ]
z 1=
X − µ σ
z 1=
z 2=
z 2=
20 −23,5 7,5
=−0,46
X − µ σ 16 −23,5 7,5
=−1
P"&$#$ili(#( s&li'i!#(# P
X ! 20 " y X ≥
E!&'es: P [ X ! 20 " y X ≥ 16 ]= 1− 2
P [ X ! 20 " y X ≥ 16 ]= 0,3413 −0,1772 =0,1641
L# *"&$#$ili(#( (e .ue u# *e"s&# .ue llegue #l "e3ugi& !eg# u# *u!u#'i, e!"e 16 5 20 *u!&s es 16-@1
@ Si l#s *e"s&#s si 7&g#" '& *u!u#'i, e el 1) +s #l!& (e$e se" ei#(#s # l&s se"i'i&s (e *"ee'i, (e sui'i(i&s- Hu4 *u!u#'i, 7#'e '#li3i'#" # u# *e"s&# .ue lleg# #l "e3ugi& *#"# es!e se"i'i&
E es!e '#s& se .uie"e .ue # *#"!i" (e l# *"&$#$ili(#( & *&"'e!#%e (#(& lleg#" #l J+e"& & #l&" (e K
Se (es*e%# K =
X − µ (&(e X =( σ ) + # σ
X =( σ ) + # =( 0,38∗7,5 )+ 23,5=26,35
L# *u!u#'i, (e u# *e"s&# .ue lleg# #l "e3ugi& 5 se# ei#(# #l se"i'i& (e *"ee'i, (e sui'i(i& es l# '#li3i'#'i, (e 26-=) & +#s
) L#s *e"s&#s si 7&g#" '& *u!#'i, e el 2) +s $#%&- se le e# # u se"i'i& (e &"ie!#'i, l#$&"#l *#"# +e%&"#" sus "e'u"s&s Hu4 *u!u#'i, *e"+i!e '#li3i'#" # u# *e"s&# *#"# #''e(e" # es!e se"i'i&
Es!e *u!& es igu#l #l #!e"i&" .ue # *#"!i" (e l# *"&$#$ili(#( & *&"'e!#%e (#(& lleg#" #l J+e"& & #l&" K
=
X − µ (&(e X =( σ ) + # σ
X =( σ ) + # = (−0,67∗7,5 )+ 23,5 =18,47
L# *u!u#'i, (e u# *e"s&# .ue lleg# #l "e3ugi& 5 .ue se# ei#(# #l se"i'i& (e &"ie!#'i, l#$&"#l es (e: 1-)? & +e&s
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