> >@=Q5@ bjbj22 "hXX;;;8;4<ir~
=^h="======qqqqqqq$sR9vr%A==%A%Ar==#r'C'C'C%Ap==q'C%Aq'C'C?Ci(n=< v;Ak4o9r0irkPvqBvh(n`^v(n=>h'C>T>M===rr7:C:KING FAHD UNIVERSITY OF PETROLEUM & MINERALS
DEPARTMENT OF MATHEMATICAL SCIENCES
DHAHRAN, SAUDI ARABIA
STAT 319: PROBABILITY & STATISTICS FOR ENGINEERS & SCIENTISTS
Final Exam, Semester043 (2005)
Time: 7:00 pm to 9:30 pm. Tuesday, August 23, 2005
Instructor: Musawar Amin Malik
Student Name: ID# Section #
______________________________________________________________________
Answer all questions. You are allowed to use any electronic calculator.
Question No MarksMarks Obtained12
22
32
44
5
462
72
87+1+2
95+2
104+2+2
116+3
12
7+2+2+6+6Total
75
Discuss the circumstances under which you would prefer the median to the mean as a measure of location.
Considering the relative positions of the mean, median and mode, draw a right skewed distribution and label the three measures of location.
Is it appropriate to compare the standard deviations of two or more distributions with different means? If not what measure is more appropriate?
A machine produces bolts which are 10 % defective. Find the probability that in a random sample of 400 bolts produced at most 35 of the bolts will be defective.
A population has a mean of 1.35 and a standard deviation of 0.40. If a random sample of 49 items is selected from the population calculate the probability that the sample mean will be no more than 1.45.
A CBS News survey reported that 67% of adults said the U. S. Treasury should continue making pennies. If six adults are selected at random, determine the expected number of adults who will say the U. S. Treasury should continue making pennies.
An auto parts store in the city believes that it has parts in inventory to meet the needs of 90% of its customers. If a random sample of 10 customers is selected, what is the probability that the store will have parts for all of them?
In an air pollution study, ozone measurements were taken in a large California city at 5.00 P.M. The eight readings (in parts per million) were:
7.9 11.3 6.9 12.7 13.2 8.8 9.3 10.6
a. Find a 99% confidence interval for the corresponding true mean.
b. What assumption do you need to do part a.
c. Are you comfortable with the statement that the mean is 10.5? Why?
A manufacturer of electronic calculators is interested in estimating the fraction of defective units produced. A random sample of 1200 calculators contains 15 defectives.
Formulate and test an appropriate hypothesis to determine if the fraction defective exceeds 0.01 at the 0.05 level of significance. Interpret your conclusion.
How large a sample is required if we want to be 95 % confident that our estimate is within 0.04?
Agricultural experts in Sweden have developed a new method of irrigation, called
fertigation, in which fertilizer is added to water and the mixture is dripped
periodically onto the roots of the plants. Very little water is wasted, and the
nutrients go directly where they are needed. To test this new process, 100 acres
were randomly selected and their historical yields were recorded. The fertigation
process was then applied to the new crop and the new yields were recorded. The
accompanying table summarizes the results.
Before Fertigation After Fertigation
Sample size 100 100
Mean Yield 40% 75%
Standard Deviation 8% 6%
a. Estimate the difference between the true mean yields before and after fertigation.
Use a 90% confidence interval.
b. Interpret the confidence interval of part (a).
c. Can you use your result of part (a) to test the hypothesis that there is no difference
between the true mean yields before and after the fertigation at 5% level of
significance? Why?
Two companies that manufacture batteries for electronics products have submitted their products to an independent testing agency. The agency tested 25 of each companys batteries and recorded the length of time the batteries lasted before failure. The following results were deter mined:
Company A Company B
EMBED Equation.3 hours EMBED Equation.3 hours
s = 3.6 s = 5.0
a. Conduct the test for the difference between the average lives of the batteries for the
two companies, assuming equal population variances for the batteries of two
companies. ( use alpha 1 %).
b. Find the pvalue of your test in part a.
The following are data on the drying time of a certain varnish and the amount of an additive that is intended to reduce the drying time:
Ammount of varnish additive (grams)
x012345678Drying time (hours)
y12.010.510.08.07.08.07.58.59.0(y = 80.5, (y EMBED Equation.3 = 740.75, (x = 36, (x EMBED Equation.3 = 204 and (x y = 299,
EMBED Equation.3 = 1.35
Calculate the least square estimates of the slope and intercept of a simple linear regression model. Graph the regression line.
Use the equation of the estimated line to predict the drying time when the amount of varnish additive is 6.6 grams.
What change in drying time would be expected for one gram change in varnish additive.
Calculate the coefficient of correlation and coefficient of determination and interpret these values.
Find a 98% confidence interval for the conditional mean of drying time when the varnish additive is 6.6 grams.
PAGE
PAGE 1
ghi c d ;
<
=
>
B
D
E
I
ºvfb^^b^hh
hFhh
h v6CJOJQJ]hc5CJOJQJ\hcCJOJQJaJhc5CJOJ\h;sCJOJh
CJOJhk/CJOJhcCJOJhxRCJOJhcCJOJQJhc56CJOJQJ\]hc hc5CJOJQJ\^JaJhc5OJQJ\^JaJ$Qghi c d
"
)
8
!~!~!~!A!!!!!!!!!!!!!1!0 $Ifgd6gdcgdh
gdc@&gdc $@&a$gd{$a$gdc $@&a$gdc$a$gdc $@&a$gdc8
9
;
=
>
?
zn0bbY $Ifgd6$$Ifa$gd6$$Ifa$gdh
kd$$IflFbj 04
la?
@
B
D
E
F
zYn0bVM $Ifgd6$$Ifa$gd6$$Ifa$gdF$$Ifa$gdh
kd$$IflFbj 04
laF
G
I
K
L
M
zYn0bbY $Ifgd6$$Ifa$gd6$$Ifa$gdh
kdZ$$IflFbj 04
laI
J
K
L
N
O
P
Q
R
S
U
X
Y
]
^
_
`
a
c
d
e
f
g
h
j
k
l
q
r
s
u
v
w
x
z
~
!#&*2SYZ]
h30h%'hph{hoh^hEh_q[h}[h;khFhn3hRThchh
MM
N
P
R
S
T
zYn0bbY $Ifgd6$$Ifa$gd6$$Ifa$gdh
kd$$IflFbj 04
laT
U
W
X
Z
[
zYn0n0bY $Ifgd6$$Ifa$gd6$$Ifa$gdh
kd$$IflFbj 04
la[
\
^
`
a
b
zYn0bbY $Ifgd6$$Ifa$gd6$$Ifa$gdh
kda$$IflFbj 04
lab
c
e
g
h
i
zYn0bbY $Ifgd6$$Ifa$gdn3$$Ifa$gdh
kd$$IflFbj 04
lai
j
l
r
s
t
zYn0bbY $Ifgd6$$Ifa$gd6$$Ifa$gdh
kd$$IflFbj 04
lat
u
w
{

}
zYn0bYP $Ifgd6 $Ifgdh
$$Ifa$gd6$$Ifa$gdh
kdh$$IflFbj 04
la}
~
zYn0bbY $Ifgd6$$Ifa$gd6$$Ifa$gd^kd$$IflFbj 04
la
zYn0bbY $Ifgd6$$Ifa$gd6$$Ifa$gd^kd$$IflFbj 04
la
zYn0e0Ye $$Ifa$gd6 $Ifgd6$$Ifa$gd^kdo$$IflFbj 04
la
zYq0q0eq $$Ifa$gd6 $Ifgd6kd$$IflFbj 04
la
!"zYu!m!h!h!h!h!h!h!h!h!h!gd%'
&Fgdpgdm&kd$$IflFbj 04
la"#$%&STUVWXY!!!!!!!!!!!!!!!!!!!!!!!!!!!!
&Fgdpgd%'YZ[\]
!!!!!!!!!!!!!!!!!!!!!!!!!!!gdF
&Fgdpgd%'
\]!!!!!!!!!!!!!!!!!!!!!!!!gd5i$h^ha$gd5ih^hgd5i
&Fgd%'
&Fgdpgd%'
[\%&'lqrqr<=CSWjoFJhisuz{vx־ֺֺֺhQh%'hWc5hfh{hlxhRPhWchRh5ihU
h%'hFh%'h30hphU
hpI !"#$%&l!!!!!!!!!!!!!!!!!!!!!!!!!!!!!gd5ilmnopqr!!!!!!!!!!!!!!!!!!!!!!!!!!
&Fgdlxgdlx
&Fgd{gd5i=>?@ABCK!!!!!!!!!!!!!!!!!!!!!!!!!gdWcgd30
&Fgd30gd{
&FgdWcgdlxc>Fijklmnopqrstuvwxyz!!!!!!!!!!!!!!!!!!!!!!!!!!!!$a$gdWcgdWcz{`wx2>_`ab!!!!!!!!!!!!!!!!!\K!!!!!!!!gdf$a$gdfh^hgd%'
&Fgd30gdm&gdWcx()*+ABL^`}45noɼ~u~uhh
hQaJ jShh
hQaJhh
h30hlxh%'hU
h30jhU
hfEHUjӡF
hU
hfUVjv hU
hfEHUjӡF
hU
hfUVjhU
hfUhU
hf5hU
h%'hfhQhU
hf+bcdefghijklmnopqrstuvwxyz{}!!!!!!!!!!!!!!!!!!!!!!!!!!!!!gdf56Z\^`bdfhjlno!!!!Ffk $IfgdE$$Ifa$gdEgdQ
&Fgd%'gdf5Y!!!!!!!!!!!!!!!!!!!!!!gdlx
&FgdlxgdQFf. $IfgdE
*+,./5ABFG鮟钃}}yuququyhu_yhlxhlxaJhlxhQaJh{hlxhQ
hlxaJjhh
hlxEHUaJj]F
hlxCJUVjhh
hQEHUaJj@
hh
hQUVaJ jShh
hQaJjRhh
hQEHUaJjx@
hh
hQUVaJhh
hQaJjhh
hQUaJ%BCDEFG
!!!!!!!!!!!!!!!!!!!!!!!!!!!
&Fgdlx
&FgdQgdlxh vh{0JmHnHuh}r
h}r0Jjh}r0JUhkhU
hfhfhthoh{hlxhlxhQaJhQhlxhlxaJ !!!!!!!!!!!!!!!!!!h]hgd&P&`#$gd vgdm&gdf
&FgdQgdlx!gdm& 1h/ =!"#$%$$If!vh555 #v#v#v :Vl0555 4a$$If!vh555 #v#v#v :Vl0555 4a$$If!vh555 #v#v#v :Vl0555 4a$$If!vh555 #v#v#v :Vl0555 4a$$If!vh555 #v#v#v :Vl0555 4a$$If!vh555 #v#v#v :Vl0555 4a$$If!vh555 #v#v#v :Vl0555 4a$$If!vh555 #v#v#v :Vl0555 4a$$If!vh555 #v#v#v :Vl0555 4a$$If!vh555 #v#v#v :Vl0555 4a$$If!vh555 #v#v#v :Vl0555 4a$$If!vh555 #v#v#v :Vl0555 4a$$If!vh555 #v#v#v :Vl0555 4a$$If!vh555 #v#v#v :Vl0555 4a*Dd
[Tb
c$A??3"`?2t*q~uP b`!H*q~u` SXJxڅQ=KA7I\.~@:RhIe
0[+USǻԁ;MUӪӣEl"&i٤K)
蚌9)^Zr/~I+Vڋ
b$ς_mqGphh]ѫW>e&2M&Ir5p\+2zAٷ#nqYz>//xjo!08t:ٝQ9,[lAv?Lbo0Fe,Dd
[Tb
c$A??3"`?2voz&8G!Rb`!Joz&8G!` SXJxcdd``$D@9@, fbd02,(1dbfaR`J`41u@Tv7$# _L QbS%d7S? `731d++&10܆0f`
L@(\1 H'0b!&1Ma`8L^eNF&&\t1F$$If!v
h5 55555555 5
#v #v
:Vl
t"65 5
"kd
$$Ifl
$ d4t"
t0"6((
!"#$%&'()*+,./012346789:;<K?BCDFEGIHJPLMNOSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{}~Root Entry FfvA
Data
5WordDocument"hObjectPool vfv_1185010594FvvOle
CompObjfObjInfo !#$%&')
FMicrosoft Equation 3.0DS EquationEquation.39q(II
x=41.5
FMicrosoft Equation 3.0DS EqEquation Native D_1185010579FvvOle
CompObj
fuationEquation.39q(tI(I
x=39.0
FMicrosoft Equation 3.0DS EquationEquation.39qObjInfo
Equation Native
D_1082622328Fv`vOle
CompObj
fObjInfoEquation Native 4_1082622350F`v`v,IoI
2
FMicrosoft Equation 3.0DS EquationEquation.39q,IhI
2
FMicrosoft Equation 3.0DS EqOle
CompObjfObjInfoEquation Native 4_1185439148F`v`vOle
CompObjfObjInfouationEquation.39qN$II
SY.XZOh+'0 $0
LX
dpxKING FAHD UNIVERSITY OF PETROLEUM & MINERALSd 1INGITC/ACSTC/TC/NormEquation Native @1TableR?wSummaryInformation(DocumentSummaryInformation8"H((44
la$$If!v
h5 55555555 5
#v #v
:Vl
t"65 5
"kd$$Ifl
$ d4t"
t0"6((((44
laDd
,J
CA?"2%Dr6詿
Reb`!Dr6詿
Rex5O;
P V.=,ZD$0VPJSp,w~[S R5GFFnYGOXvv,+%\eD!6hgF#̙]o
M;}aԕD%.BX<@j#4V%ZxY'$'Xrnkny)"~wr͕H}+Dd
hb
c$A??3"`?2Nb@T?@BDEFGIKLMNPRSTUWXZ[\^`abceghijlrstuw{}~ !"#$%&STUVWXYZ[\]
\] ! " # $ % & l m n o p q r
=>?@ABCK
c
>Fijklmnopqrstuvwxyz{`wx2>_`abcdefghijklmnopqrstuvwxyz{}56Z\^`bdfhjlno5BCDEFG
0000Q0Q00i000000000000 0 0 0 0 00 0 0 0 00 0 0 0 00 0 0 0 00 0 0 00 0 0 0 0 00 0 0 0 00 0 0 0 00 0 0 0 00 0 0 0 00 0 0 0 00 0 0 00 0 0 0 00 0 0 0 0 00000000000000 00000000000000000 00000000000 0000000000p000000 00000000000p000000 0000 0 00000000000000000000000000000000000000000000 00 0r 000000000000p00000000p0000000000p0 0r 000000 0 0000000000000000000000000p0000000000000000000 0
000000000000000000000000000000000000000000 0000 0 0 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 0 0 00 00000000000p0p00000000p00p000p0 000000 0 00000000000000000000000000 00000p0000000L0bcehijO900zmO900z O900 Oy00 O900 0T 0zwI
x%+/18
?
F
M
T
[
b
i
t
}
"Y
lzb !"#$&'()*,.023(**,:::::!!
VLLL&7&Lԓ7ՓL֓K
BsF*S ;g7YB(la\QMavk^rY_xnof_ ff䓔Nmloq]
FMr _0s@7$OP*^`o(.^`.pLp^p`L.@@^@`.^`.L^`L.^`.^`.PLP^P`L.^`o(.^`.pLp^p`L.@@^@`.^`.L^`L.^`.^`.PLP^P`L.^`o(.^`.pLp^p`L.@@^@`.^`.L^`L.^`.^`.PLP^P`L.^`o(.
^`hH.
pLp^p`LhH.
@@^@`hH.
^`hH.
L^`LhH.
^`hH.
^`hH.
PLP^P`LhH.hh^h`o(.hh^h`o(.^`o(.^`.pLp^p`L.@@^@`.^`.L^`L.^`.^`.PLP^P`L.^`o(.
^`hH.
pLp^p`LhH.
@@^@`hH.
^`hH.
L^`LhH.
^`hH.
^`hH.
PLP^P`LhH.
^`OJPJQJ^J.^`o(.^`o(.
pLp^p`LhH.
@@^@`hH.
^`hH.
L^`LhH.
^`hH.
^`hH.
PLP^P`LhH.^`o(.
^`hH.
pLp^p`LhH.
@@^@`hH.
^`hH.
L^`LhH.
^`hH.
^`hH.
PLP^P`LhH.hh^h`o(.hh^h`o(^`o(.
^`hH.
pLp^p`LhH.
@@^@`hH.
^`hH.
L^`LhH.
^`hH.
^`hH.
PLP^P`LhH.^`o(.^`o(.
pLp^p`LhH.
@@^@`hH.
^`hH.
L^`LhH.
^`hH.
^`hH.
PLP^P`LhH.^`o(.
^`hH.
pLp^p`LhH.
@@^@`hH.
^`hH.
L^`LhH.
^`hH.
^`hH.
PLP^P`LhH.hh^h`o(.^`o(.
^`hH.
pLp^p`LhH.
@@^@`hH.
^`hH.
L^`LhH.
^`hH.
^`hH.
PLP^P`LhH.^`o(.
^`hH.
pLp^p`LhH.
@@^@`hH.
^`hH.
L^`LhH.
^`hH.
^`hH.
PLP^P`LhH.^`o(.hh^h`o(.^`o(.^`o(.
pLp^p`LhH.
@@^@`hH.
^`hH.
L^`LhH.
^`hH.
^`hH.
PLP^P`LhH.^`o(.
^`hH.
pLp^p`LhH.
@@^@`hH.
^`hH.
L^`LhH.
^`hH.
^`hH.
PLP^P`LhH.Qwy(6avk^ff0K γt ? j 76FCh
vm&%'k/RBV_q[Wcrnefgj;kvm}rjulxE{n3R3M$ vRT6RP^qTBs;305i%p
&P4~/k^ctpo}[OQje;s'xRd")89;>?@BEFGILMNPSTUXZ[\^abcehijlstuw}~r
C456\^`bdfhjlnoa0@@@@@&mP@UnknownG:Times New Roman5Symbol3&:Arial9CG Times?5 :Courier NewM`@Traditional Arabic"qh2z&
* *!>4d3QH)?c,KING FAHD UNIVERSITY OF PETROLEUM & MINERALSITC/ACSITC/ACSh
CompObj(j
FMicrosoft Word Document
MSWordDocWord.Document.89q