MTH 380 Lecture Notes - Lecture 8: Urt, Awi People, Protein Kinase B
8 views19 pages
ttuffr-l-
e4
h/t =Es
ho?ulrlr't
o&^ 'i : L5.f
Gve t{", W4
cpl*u,/.l.klLr
ouVA 9a = l0 't '
h,tkfu,:i?€-
S4rt -raw+ll ixts u
W W"d'-,A d1*4
96o/o 2s.l
4. 16L,=
rlh
ft *"N'tk rne'a/Yl' 3c =
; Lqg olo r,urym !'tmr)'s
4.368 =fod
po4n+ av[h^'k
hr,"t tn %
x U,,vW v5,,*1" ry L;' \,(^I-' ryr-
ft $,t^/L*v^ '4^ 4''t^ % h = Lo a 'a t'v| ltt' 0' Awlt n"^^'"^''^ig
gt*' n'' n il)il" wu;*rqa- t,n wr,'n'A c)""n"*t vo'l'M'&-?tfuq'
-rL,8 ,7,4 r t. 19T
An tr^rtr^ac t*{1n, m/t{ % Y,*W;v ff"c1y'"t'+tfi ln84 h
It^l p"^+ lztuwutA,Va,W;Wa Ela,urlS-a )-p"lA'h-0'1'L eg S" 6'/o-
b,tVvaw4 t4,.p ,,"r^^ P*t r^+ ry fW to411t/1X at 'u'** VlAl
Ft v.-at tr^r ,-?/*1,W\O,l<
Vtl*ri rv\
vk^ILe
Awi
H,.
I1^, p-^l q4l4watW *6 ['t^, v{'-u,fr W ttM/N#el tvr *\,,
rt,tm,,,-t ,^0.-a, a-^n- -lJ^a A,..,1 l', ..^.^lI h,t r|,lr@et-t'f1 tW"{'ta{
urt^^^^*r@_ry-{4^0 Ws+tz V"Lvvt4^^ tr W [-0t] tt'r,
3 Sn/, vr q -fla-+vt-='1.96 = 4,56
o(ir.E,z , Ltr P. Lq(' ft*'h"+^n-
$ou wo-,a* fi q*hwvyr4. W yrrr^* l"*; uail;4 del.,,l I.*"
b+,o,d*A t'h/,t huu@ drL rt rrfi;U;4rt . '
[, =-- - , U /. __- : l r
dl^Artt^ a* @ w't4r1 |^ll,'L iua^fr$-t =3|'unt*t
dtu^ s =5 wryt2^WW-, (o\lu4,t( {fu w,la,4^ Irn,o;"/t1u ilWqTfu,
W o,t^A c.aJn)s,k WrWy* % Nrp
ou,n/tA Vf hNA[
'L;.:o+ Fut,tt e'kkvvLa4< (* rn*a'fiu h,a,^,*Vfu.{a
a- Bd-{,,lr/>' 1'4M+ *^*a//kt^4-\ err
!
i = 3\ enulrcg P* lr,r.t/-'
o,;r#..6at"t ic ts
gfalo wa,rf* % l/ri?r is 4. q6 5-
{T =1. gG 3 ={,rn)
{too \/
Wv* vt<t"2fl" S
';*r*"u*4,rr WvtA % o*a^. P LL( ,rury<**.
Nu H^r 4 _% tt^i zt4- 6"*up*-i "dt ,a*i^ atwiwan
tval P"t ttnla *%.YYry,Y::Y
it U". a,rvv;' )'o't' <nut\vu) ?Y% t1^'L b"q
'#w)ilfr':ffih
oL lg.3uarnt4o trutt"{4 q' M d)-vtov?Iout'
U ';: ;';'r"ilu\r&"wa/'+4- I{u t+'ur vtr}*'u h'w' *'w|
J, t ilt, o -' V n v,lbt*vat ut o t, "
A p{4vv(- urrj;uLe^^< a*Wuh'\!'aAA WW% hut is} lf,$
W,'ttu vv\tft^vr+fi4rrtf = .,1.54 fr ='l-96 H = 1.86-
o
@ Wrvr,t/1p,lt,
Example 4
W\ cy,tt\/,,Lit^/"{^/al-{"'r jtrx1a'ill,v'Uvu ttttllaAtt f .'
erfr;/"l *'is vyg-iw*l' ,'yop"th'^ voirraa^l& is bn'o\tth '
VW lr, V1,\rLCrN .
The lifetime in hours of a 75 - watt light bulb is known to be
normally distributed with standard deviation of 25 hours.
A random sample of 20bulbs has a mean life of I0L4 hours.
a. Construct a 90% Cl ,95% Cl a nd99% Cl on mean life of the bulb.
b. tf we want to be 90% (95%,99%) confident that the error in
estimating mean life is no more than 5 hours, what sample size
should be used?
a. Let X be a Iifetime (in hours) of a75 - watt Iightbulb.
We are given that X is normal random variable with unknown
meanp and sample standard deviation o = 25 hours:
X - Irr( F,o2)
Sampte size n =20 is small (n= 20 <30).
lf population is normal and population variance and
standard deviation are known, s0mpling distribution is
normal for any sampIe size:
o