Business Statistics: A First Course The Normal...
44
Business Statistics: A First Course, 5e © 2009 Prentice-Hall, Inc. Chap 6-1 Chapter 6 The Normal Distribution Business Statistics: A First Course 5 th Edition
Transcript of Business Statistics: A First Course The Normal...
Busin
ess S
tatistics: A
First C
ours
e, 5e ©
2009 P
rentice-H
all,
Inc.
Chap 6
-1
Ch
ap
ter
6
The N
orm
al D
istr
ibutio
n
Busin
ess S
tatistics:
A F
irst C
ou
rse
5th
Ed
itio
n
Busin
ess S
tatistics: A
First C
ours
e, 5e ©
2009 P
rentice-H
all,
Inc..
Chap 6
-2
Lea
rnin
g O
bje
ctives
In t
his
ch
ap
ter,
yo
u learn
:
�T
o c
om
pu
te p
rob
ab
ilitie
s f
rom
th
e n
orm
al
dis
trib
utio
n
�T
o u
se
th
e n
orm
al p
rob
ab
ility
plo
t to
de
term
ine
wh
eth
er
a s
et
of da
ta is a
pp
roxim
ate
ly n
orm
ally
dis
trib
ute
d
Busin
ess S
tatistics: A
First C
ours
e, 5e ©
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rentice-H
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Inc..
Chap 6
-3
Contin
uous P
rob
abili
ty D
istr
ibutions
�A
co
ntin
uo
us r
an
do
m v
ari
ab
leis
a v
ari
ab
le t
ha
t
ca
n a
ssum
e a
ny v
alu
e o
n a
co
ntin
uu
m (
ca
n
assu
me
an
un
co
un
tab
le n
um
be
r o
f va
lue
s)
�th
ickness o
f an ite
m
�tim
e r
equir
ed t
o c
om
ple
te a
task
�te
mpera
ture
of
a s
olu
tion
�he
ight, in inches
�T
he
se
ca
n p
ote
ntia
lly t
ake
on
an
y v
alu
e
de
pe
nd
ing
on
ly o
n t
he
ab
ility
to
pre
cis
ely
an
d
accu
rate
ly m
ea
su
re
Busin
ess S
tatistics: A
First C
ours
e, 5e ©
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rentice-H
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Inc..
Chap 6
-4
The N
orm
al D
istr
ibution
�‘B
ell S
hap
ed
’
�S
ym
metr
ical
�M
ean
, M
ed
ian
an
d M
od
eare
Eq
ual
Lo
cati
on
is d
ete
rmin
ed
by t
he
mean
, µ
Sp
read
is d
ete
rmin
ed
by t
he
sta
nd
ard
devia
tio
n, σ
Th
e r
an
do
m v
ari
ab
le h
as a
n
infi
nit
e t
heo
reti
cal
ran
ge:
+∞ ∞∞∞
to
− −−−∞ ∞∞∞
Mean
=
Med
ian
=
Mo
de
X
f(X
)
µ
σ
Busin
ess S
tatistics: A
First C
ours
e, 5e ©
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rentice-H
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Inc..
Chap 6
-5
The N
orm
al D
istr
ibution
Density F
unction
2µ
)(X
21
e2π1
f(X
)
−
−
=σ
σ
�T
he f
orm
ula
for
the n
orm
al pro
ba
bili
ty d
ensity function is
Wh
ere
e =
th
e m
ath
emat
ical
co
nst
ant
app
rox
imat
ed b
y 2
.718
28
π=
th
e m
ath
emat
ical
co
nst
ant
app
rox
imat
ed b
y 3
.141
59
µ=
th
e pop
ula
tion
mea
n
σ=
th
e pop
ula
tion
sta
nd
ard d
evia
tion
X =
an
y v
alu
e o
f th
e co
nti
nuou
s v
aria
ble
Busin
ess S
tatistics: A
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ours
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rentice-H
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Inc..
Chap 6
-6
By v
ary
ing
th
e p
ara
mete
rs µ
an
d σ
, w
e o
bta
in
dif
fere
nt
no
rmal
dis
trib
uti
on
s
Many N
orm
al D
istr
ibution
s
Busin
ess S
tatistics: A
First C
ours
e, 5e ©
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rentice-H
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Inc..
Chap 6
-7
Th
e N
orm
al D
istr
ibu
tio
n
Sh
ap
e
X
f(X
)
µ
σ
Ch
an
gin
gµ
shifts
the
dis
trib
utio
n left o
r right.
Ch
an
gin
g σ
incre
ase
s
or
decre
ases t
he
spre
ad.
Busin
ess S
tatistics: A
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ours
e, 5e ©
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rentice-H
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Chap 6
-8
Th
e S
tan
da
rdiz
ed
No
rma
l
�A
ny
no
rma
l d
istr
ibu
tio
n (
with
an
y m
ea
n a
nd
sta
nd
ard
de
via
tio
n c
om
bin
atio
n)
ca
n b
e
tra
nsfo
rme
d in
to t
he
sta
nd
ard
ize
d n
orm
al
dis
trib
utio
n (
Z)
�N
ee
d t
o t
ran
sfo
rm
X
un
its in
to
Z
units
�T
he
sta
nd
ard
ize
d n
orm
al d
istr
ibu
tio
n (
Z)
ha
s a
m
ea
n o
f 0
an
d a
sta
nd
ard
de
via
tio
n o
f 1
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ess S
tatistics: A
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ours
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rentice-H
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Inc..
Chap 6
-9
Tra
nsla
tio
n to
th
e S
tan
da
rdiz
ed
N
orm
al D
istr
ibu
tio
n
�T
ran
sla
te f
rom
X t
o t
he
sta
nd
ard
ize
d n
orm
al
(th
e “
Z”
dis
trib
utio
n)
by s
ub
tra
ctin
g t
he
me
an
of
X a
nd
div
idin
g b
y its
sta
nd
ard
de
via
tio
n:
σ
µX
Z−
=
Th
e Z
dis
trib
utio
n a
lwa
ys h
as m
ea
n =
0 a
nd
sta
nd
ard
de
via
tio
n =
1
Busin
ess S
tatistics: A
First C
ours
e, 5e ©
2009 P
rentice-H
all,
Inc..
Chap 6
-10
The S
tand
ard
ized N
orm
al
Pro
ba
bili
ty D
ensity F
unction
�T
he
fo
rmu
la f
or
the
sta
nd
ard
ize
d n
orm
al
pro
ba
bili
ty d
en
sity fu
nctio
n is
Where
e =
the m
ath
em
atical consta
nt
appro
xim
ate
d b
y 2
.7182
8
π=
the m
ath
em
atical consta
nt
appro
xim
ate
d b
y 3
.1415
9
Z =
an
y v
alu
e o
f th
e s
tandard
ized n
orm
al dis
trib
ution
2(1
/2)Z
e2π1
f(Z
)−
=
Busin
ess S
tatistics: A
First C
ours
e, 5e ©
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rentice-H
all,
Inc..
Chap 6
-11
Th
e S
tan
da
rdiz
ed
No
rma
l D
istr
ibu
tio
n
�A
lso k
now
n a
s the “
Z”
dis
trib
ution
�M
ean is 0
�S
tandard
Devia
tion is 1
Z
f(Z
)
0
1
Va
lues a
bo
ve t
he m
ean h
ave p
ositiv
eZ
-valu
es,
valu
es b
elo
w t
he m
ean h
ave n
eg
ative
Z-v
alu
es
Busin
ess S
tatistics: A
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ours
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rentice-H
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Chap 6
-12
Exam
ple
�If
X
is
dis
trib
ute
d n
orm
ally
with
me
an
of
10
0
an
d s
tan
da
rd d
evia
tio
n o
f 50
, th
e
Z va
lue
fo
r
X =
20
0is
�T
his
sa
ys t
ha
t X
= 2
00
is
tw
o s
tan
da
rd
de
via
tio
ns (
2 in
cre
me
nts
of 5
0 u
nits)
ab
ove
the
me
an
of
10
0.
2.0
501
00
20
0
σ
µX
Z=
−=
−=
Busin
ess S
tatistics: A
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ours
e, 5e ©
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rentice-H
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Inc..
Chap 6
-13
Co
mp
arin
g
X
and
Z
units
Z
10
0
2.0
0
20
0X
No
te t
hat
the s
hap
e o
f th
e d
istr
ibu
tio
n is t
he s
am
e,
on
ly t
he s
cale
has c
han
ged
. W
e c
an
exp
ress t
he
pro
ble
m in
ori
gin
al u
nit
s (
X)
or
in s
tan
dard
ized
u
nit
s (
Z)
(µ=
100, σ
= 5
0)
(µ=
0, σ
= 1
)
Busin
ess S
tatistics: A
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ours
e, 5e ©
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rentice-H
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Inc..
Chap 6
-14
Fin
din
g N
orm
al P
rob
ab
ilitie
s
ab
X
f(X
)P
aX
b(
)≤
Pro
bab
ility
is m
ea
su
red
by th
e a
rea
unde
r th
e c
urv
e
≤
Pa
Xb
()
<<
=
(Note
that
the
pro
ba
bili
ty o
f a
ny
indiv
idu
al valu
e is z
ero
)
Busin
ess S
tatistics: A
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ours
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rentice-H
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Chap 6
-15
f(X
)
Xµ
Pro
ba
bili
ty a
s
Are
a U
nd
er
the C
urv
e
0.5
0.5
The t
ota
l are
a u
nd
er
the c
urv
e is 1
.0, and t
he c
urv
e is
sym
metr
ic, so h
alf is a
bove t
he m
ean,
half is b
elo
w
1.0
)X
P(
=∞
<<
−∞
0.5
)X
P(µ
=∞
<<
0.5
µ)
XP
(=
<<
−∞
Busin
ess S
tatistics: A
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ours
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rentice-H
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Chap 6
-16
Th
e S
tan
da
rdiz
ed
Norm
al T
ab
le
�T
he
Cu
mu
lative
Sta
nd
ard
ize
d N
orm
al ta
ble
in t
he
te
xtb
oo
k (
Ap
pe
nd
ix t
ab
le E
.2)
giv
es t
he
pro
ba
bili
ty le
ss t
han
a d
esir
ed
va
lue
of
Z (
i.e
.,
fro
m n
eg
ative
in
finity to
Z)
Z0
2.0
00.9
772
Exam
ple
:
P(Z
< 2
.00)
= 0
.9772
Busin
ess S
tatistics: A
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ours
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rentice-H
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Chap 6
-17
Th
e S
tan
da
rdiz
ed
Norm
al T
ab
le
The v
alu
e w
ith
in t
he
table
giv
es t
he
pro
ba
bili
ty f
rom
Z =
− −−−∞ ∞∞∞
up t
o the d
esire
d Z
valu
e
.9772
2.0
P(Z
< 2
.00)
=0.9
772
Th
e r
ow
sho
ws
the v
alu
e o
f Z
to
the first
decim
al po
int
Th
e c
olu
mn
giv
es t
he v
alu
e o
f Z
to the s
econd d
ecim
al po
int
2.0. . .
(co
ntin
ue
d)
Z 0
.00 0
.01
0
.02
…
0.0
0.1
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ess S
tatistics: A
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ours
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Chap 6
-18
Gen
era
l P
rocedure
for
Fin
din
g N
orm
al P
roba
bili
ties
�D
raw
th
e n
orm
al cu
rve
fo
r th
e p
rob
lem
in
term
s o
f X
�T
ran
sla
te X
-va
lue
s t
o Z
-va
lue
s
�U
se
th
e S
tan
da
rdiz
ed
No
rma
l T
ab
le
To
fin
d
P(a
< X
< b
) w
he
n
X
is
dis
trib
ute
d n
orm
ally
:
Busin
ess S
tatistics: A
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ours
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rentice-H
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Chap 6
-19
Fin
din
g N
orm
al P
roba
bili
ties
�Let X
repre
sent th
e tim
e it ta
kes to
dow
nlo
ad a
n im
age file
fro
m the inte
rnet.
�S
uppose X
is n
orm
al w
ith m
ean 8
.0 a
nd
sta
ndard
devia
tion 5
.0. F
ind P
(X <
8.6
)
X
8.6
8.0
Busin
ess S
tatistics: A
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ours
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rentice-H
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Chap 6
-20
�Let
X r
epre
sen
t th
e t
ime it
takes t
o d
ow
nlo
ad
an im
age f
ile f
rom
the
inte
rnet.
�S
uppose X
is n
orm
al w
ith m
ea
n 8
.0 a
nd s
tan
dard
devia
tio
n 5
.0.
Fin
d
P(X
< 8
.6)
Z0.1
20
X8.6
8
µ=
8
σ=
10
µ=
0
σ=
1
(co
ntin
ue
d)
Fin
din
g N
orm
al P
roba
bili
ties
0.1
25
.0
8.0
8.6
σ
µX
Z=
−=
−=
P(X
< 8
.6)
P(Z
< 0
.12)
Busin
ess S
tatistics: A
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ours
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rentice-H
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Chap 6
-21
Z
0.1
2
Z.0
0.0
1
0.0
.50
00
.50
40
.50
80
.53
98
.54
38
0.2
.57
93
.58
32
.58
71
0.3
.61
79
.62
17
.62
55
So
lutio
n: F
ind
ing
P(Z
< 0
.12
)
.5478
.02
0.1
.5478
Sta
ndard
ized N
orm
al P
roba
bili
ty
Tab
le (
Port
ion)
0.0
0
= P
(Z <
0.1
2)
P(X
< 8
.6)
Busin
ess S
tatistics: A
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ours
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rentice-H
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Chap 6
-22
Fin
din
g N
orm
al
Up
pe
r T
ail
Pro
ba
bili
tie
s
�S
uppose X
is
norm
al w
ith m
ean 8
.0 a
nd
sta
ndard
devia
tion 5
.0.
�N
ow
Fin
d P
(X >
8.6
)
X
8.6
8.0
Busin
ess S
tatistics: A
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ours
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rentice-H
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Chap 6
-23
�N
ow
Fin
d P
(X >
8.6
)…
(co
ntin
ue
d)
Z
0.1
2
0Z
0.1
2
0.5
478
0
1.0
00
1.0
-0.5
478
= 0
.4522
P(X
> 8
.6)
= P
(Z >
0.1
2)
= 1
.0 -
P(Z
≤0.1
2)
= 1
.0 -
0.5
478 =
0.4
52
2
Fin
din
g N
orm
al
Up
pe
r T
ail
Pro
ba
bili
tie
s
Busin
ess S
tatistics: A
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ours
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rentice-H
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Chap 6
-24
Fin
din
g a
No
rma
l P
rob
abili
ty
Be
twe
en
Tw
o V
alu
es
�S
up
po
se
X
is
no
rma
l w
ith
me
an
8.0
an
d
sta
nd
ard
de
via
tio
n 5
.0.
Fin
d P
(8 <
X <
8.6
)
P(8
< X
< 8
.6)
= P
(0 <
Z <
0.1
2)
Z0.1
20
X8.6
8
05
88
σ
µX
Z=
−=
−=
0.1
25
88
.6
σ
µX
Z=
−=
−=Ca
lcu
late
Z-v
alu
es:
Busin
ess S
tatistics: A
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ours
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rentice-H
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Chap 6
-25
Z
0.1
2
So
lutio
n: F
ind
ing
P(0
< Z
< 0
.12
)
0.0
478
0.0
0
= P
(0 <
Z <
0.1
2)
P(8
< X
< 8
.6)
= P
(Z <
0.1
2)
–P
(Z ≤
0)
= 0
.5478 -
.500
0 =
0.0
478
0.5
000
Z.0
0.0
1
0.0
.50
00
.50
40
.50
80
.53
98
.54
38
0.2
.57
93
.58
32
.58
71
0.3
.61
79
.62
17
.62
55
.02
0.1
.5478
Sta
ndard
ized N
orm
al P
roba
bili
ty
Tab
le (
Port
ion)
Busin
ess S
tatistics: A
First C
ours
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rentice-H
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Chap 6
-26
�S
uppose X
is
norm
al w
ith m
ean 8
.0 a
nd
sta
ndard
devia
tion 5
.0.
�N
ow
Fin
d P
(7.4
< X
< 8
)
X
7.4
8.0
Pro
ba
bili
ties in t
he L
ow
er
Tail
Busin
ess S
tatistics: A
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ours
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rentice-H
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Chap 6
-27
Pro
ba
bili
ties in t
he L
ow
er
Tail
Now
Fin
d P
(7.4
< X
< 8
)…
X7.4
8.0
P(7
.4 <
X <
8)
= P
(-0.1
2 <
Z <
0)
= P
(Z <
0)
–P
(Z ≤
-0.1
2)
= 0
.5000 -
0.4
522 =
0.0
47
8
(co
ntin
ue
d)
0.0
478
0.4
522
Z-0
.12
0
The N
orm
al dis
trib
utio
n is
sym
metr
ic, so t
his
pro
bab
ility
is
the s
am
e a
s P
(0 <
Z <
0.1
2)
Busin
ess S
tatistics: A
First C
ours
e, 5e ©
2009 P
rentice-H
all,
Inc..
Chap 6
-28
Em
pir
ical R
ule
s
µ±
1σ
en
clo
ses a
bo
ut
68.2
6%
of
X’s
f(X
)
Xµ
µ+
1σ
µ-1σ
Wh
at
ca
n w
e s
ay a
bo
ut
the
dis
trib
utio
n o
f va
lue
s
aro
un
d t
he
me
an
?
Fo
r a
ny n
orm
al d
istr
ibu
tio
n:
σσ 6
8.2
6%
Busin
ess S
tatistics: A
First C
ours
e, 5e ©
2009 P
rentice-H
all,
Inc..
Chap 6
-29
The E
mpiric
al R
ule
�µ
±2σ
co
ve
rs a
bo
ut
95
%o
f X
’s
�µ
±3σ
co
ve
rs a
bo
ut
99
.7%
of
X’s
xµ
2σ
2σ
xµ
3σ
3σ
95.4
4%
99.7
3%
(co
ntin
ue
d)
Busin
ess S
tatistics: A
First C
ours
e, 5e ©
2009 P
rentice-H
all,
Inc..
Chap 6
-30
�S
teps to fin
d the X
valu
e for
a k
now
n
pro
babili
ty:
1.
Fin
d th
e Z
va
lue
fo
r th
e k
no
wn
pro
ba
bili
ty
2.
Co
nve
rt t
o X
un
its u
sin
g th
e f
orm
ula
:
Giv
en a
No
rmal P
roba
bili
tyF
ind t
he X
Valu
e
Zσ
µX
+=
Busin
ess S
tatistics: A
First C
ours
e, 5e ©
2009 P
rentice-H
all,
Inc..
Chap 6
-31
Fin
din
g t
he X
valu
e f
or
a
Know
n P
roba
bili
ty
Exa
mp
le:
�Let
X r
epre
sent
the tim
e it ta
kes (
in s
econ
ds)
to
do
wn
load a
n im
ag
e f
ile f
rom
the inte
rnet.
�S
up
pose X
is
norm
al w
ith m
ean 8
.0 a
nd s
tand
ard
devia
tion 5
.0
�F
ind X
such t
hat 20%
of
dow
nlo
ad t
imes a
re less t
han
X.
X?
8.0
0.2
000
Z?
0
(co
ntin
ue
d)
Busin
ess S
tatistics: A
First C
ours
e, 5e ©
2009 P
rentice-H
all,
Inc..
Chap 6
-32
Fin
d t
he Z
valu
e f
or
20
% in
the L
ow
er
Ta
il
�2
0%
are
a in
th
e low
er
tail
is c
onsis
ten
t w
ith
a
Z v
alu
e o
f -0
.84
Z.0
3
-0.9
.17
62
.17
36
.20
33
-0.7
.23
27
.22
96
.04
-0.8
.2005
Sta
ndard
ized N
orm
al P
roba
bili
ty
Tab
le (
Port
ion)
.05
.17
11
.19
77
.22
66
… … … …
X?
8.0
0.2
000
Z-0
.84
0
1.
Fin
d th
e Z
va
lue
fo
r th
e k
no
wn
pro
ba
bili
ty
Busin
ess S
tatistics: A
First C
ours
e, 5e ©
2009 P
rentice-H
all,
Inc..
Chap 6
-33
2.
Co
nve
rt t
o X
un
its u
sin
g th
e f
orm
ula
:
Fin
din
g t
he X
valu
e
80
.3
0.5)
84
.0
(0.
8
Zσ
µX
=
−+
=
+=
So 2
0%
of th
e v
alu
es f
rom
a d
istr
ibutio
n
with m
ean 8
.0 a
nd s
tandard
devia
tion
5.0
are
less than 3
.80
Busin
ess S
tatistics: A
First C
ours
e, 5e ©
2009 P
rentice-H
all,
Inc..
Chap 6
-34
Evalu
ating N
orm
alit
y
�N
ot a
ll con
tin
uo
us d
istr
ibu
tio
ns a
re n
orm
al
�It is im
po
rta
nt to
eva
lua
te h
ow
we
ll th
e d
ata
se
t is
a
pp
roxim
ate
d b
y a
no
rma
l d
istr
ibu
tio
n.
�N
orm
ally
dis
trib
ute
d d
ata
sh
ou
ld a
pp
roxim
ate
th
e
the
ore
tica
l n
orm
al d
istr
ibu
tio
n:
�T
he
norm
al d
istr
ibu
tion
is b
ell
sha
ped
(sym
me
tric
al)
whe
re th
e m
ean
is e
qua
l to
the
med
ian
.
�T
he
em
piric
al ru
le a
pplie
s to
the
norm
al d
istr
ibu
tio
n.
�T
he
in
terq
ua
rtile
ra
nge
of a
no
rmal d
istr
ibu
tion
is 1
.33
sta
ndard
devia
tion
s.
Busin
ess S
tatistics: A
First C
ours
e, 5e ©
2009 P
rentice-H
all,
Inc..
Chap 6
-35
Evalu
ating N
orm
alit
y
Co
mp
ari
ng
da
ta c
ha
racte
ristics to
th
eore
tica
l
pro
pe
rtie
s
�C
onstr
uct chart
s o
r gra
phs
�F
or
sm
all-
or
mo
dera
te-s
ize
d d
ata
se
ts, co
nstr
uct a s
tem
-an
d-l
ea
f d
isp
lay o
r a
bo
xp
lotto
ch
eck for
sym
metr
y
�F
or
larg
e d
ata
sets
, d
oes th
e h
isto
gra
m o
r p
oly
go
n a
pp
ear
be
ll-sh
ap
ed
?
�C
om
pute
descriptive s
um
mary
measure
s
�D
o th
e m
ea
n, m
ed
ian
an
d m
od
e h
ave
sim
ilar
va
lue
s?
�Is
the
in
terq
ua
rtile
ra
nge
ap
pro
xim
ate
ly 1
.33
σ?
�Is
the
ra
ng
e a
pp
roxim
ate
ly 6
σ?
(co
ntin
ue
d)
Busin
ess S
tatistics: A
First C
ours
e, 5e ©
2009 P
rentice-H
all,
Inc..
Chap 6
-36
Evalu
ating N
orm
alit
y
Co
mp
ari
ng
da
ta c
ha
racte
ristics to
th
eore
tica
l
pro
pe
rtie
s
�O
bserv
e the d
istr
ibutio
nof th
e d
ata
set
�D
o a
pp
roxim
ate
ly 2
/3 o
f th
e o
bserv
atio
ns lie
with
in m
ea
n ±
1
sta
nd
ard
de
via
tio
n?
�D
o a
pp
roxim
ate
ly 8
0%
of th
e o
bserv
ation
s lie
with
in m
ea
n
±1
.28 s
tan
da
rd d
evia
tio
ns?
�D
o a
pp
roxim
ate
ly 9
5%
of th
e o
bserv
ation
s lie
with
in m
ea
n ±
2
sta
nd
ard
de
via
tio
ns?
�E
valu
ate
norm
al pro
bab
ility
plo
t
�Is
the
no
rma
l p
rob
ab
ility
plo
t a
pp
roxim
ate
ly lin
ea
r (i
.e. a
str
aig
ht
line
) w
ith
positiv
e s
lop
e?
(co
ntin
ue
d)
Busin
ess S
tatistics: A
First C
ours
e, 5e ©
2009 P
rentice-H
all,
Inc..
Chap 6
-37
Co
nstr
uctin
g
A N
orm
al P
roba
bili
ty P
lot
�N
orm
al p
rob
ab
ility
plo
t
�A
rrange d
ata
into
ord
ere
d a
rray
�F
ind c
orr
espon
din
g s
tand
ard
ize
d n
orm
al qu
antile
valu
es (
Z)
�P
lot th
e p
air
s o
f poin
ts w
ith o
bserv
ed d
ata
valu
es (
X)
on t
he v
ert
ical a
xis
an
d t
he s
tand
ard
ized n
orm
al
qua
ntile
va
lues (
Z)
on the h
orizonta
l a
xis
�E
va
luate
the p
lot
for
evid
ence o
f lin
eari
ty
Busin
ess S
tatistics: A
First C
ours
e, 5e ©
2009 P
rentice-H
all,
Inc..
Chap 6
-38
A n
orm
al p
rob
ab
ility
plo
t fo
r d
ata
fro
m a
no
rma
l d
istr
ibu
tio
n w
ill b
e
ap
pro
xim
ate
ly lin
ea
r:
30
60
90
-2-1
01
2Z
XTh
e N
orm
al P
rob
abili
ty P
lot
Inte
rpre
tatio
n
Busin
ess S
tatistics: A
First C
ours
e, 5e ©
2009 P
rentice-H
all,
Inc..
Chap 6
-39
No
rma
l P
rob
ab
ility
Plo
t
Inte
rpre
tatio
n
Le
ft-S
ke
we
dR
igh
t-S
ke
we
d
Re
cta
ng
ula
r
30
60
90
-2-1
01
2Z
X
(co
ntin
ue
d)
30
60
90
-2-1
01
2Z
X
30
60
90
-2-1
01
2Z
XN
onlin
ear
plo
ts
indic
ate
a d
evia
tion
from
norm
alit
y
Busin
ess S
tatistics: A
First C
ours
e, 5e ©
2009 P
rentice-H
all,
Inc..
Chap 6
-40
Evalu
ating N
orm
alit
yA
n E
xam
ple
: M
utu
al F
unds R
etu
rns
40
30
20
10
0-10
Return 2006
Boxplot of 2006 Returns
Th
e b
oxp
lotap
pe
ars
re
ason
ab
ly s
ym
me
tric
, w
ith
fo
ur
low
er
ou
tlie
rs a
t
-9.0
, -8
.0, -8
.0, -6
.5 a
nd
on
e u
pp
er
outlie
r a
t 35
.0.
(Th
e n
orm
al d
istr
ibu
tio
n is
sym
me
tric
.)
Busin
ess S
tatistics: A
First C
ours
e, 5e ©
2009 P
rentice-H
all,
Inc..
Chap 6
-41
Evalu
ating N
orm
alit
yA
n E
xam
ple
: M
utu
al F
unds R
etu
rns
Descri
ptive
Sta
tistics
(co
ntin
ue
d)
•T
he m
ean (
12.5
142)
is s
lightly less t
ha
n t
he
media
n (
13.1
).
(In a
norm
al dis
trib
ution t
he
mean a
nd m
ed
ian a
re e
qua
l.)
•T
he inte
rquart
ilera
nge o
f 9.2
is a
ppro
xim
ate
ly
1.4
6 s
tandard
devia
tions.
(In
a n
orm
al
dis
trib
ution t
he inte
rqu
art
ilera
nge is 1
.33
sta
ndard
devia
tions.)
•T
he r
ange o
f 44 is e
qua
l to
6.9
9 s
tandard
devia
tions.
(In
a n
orm
al d
istr
ibution t
he r
ang
e is
6 s
tandard
devia
tions.)
•72.2
% o
f th
e o
bserv
atio
ns a
re w
ithin
1 s
tan
dard
devia
tion o
f th
e m
ean.
(In
a n
orm
al dis
trib
ution
this
perc
enta
ge is 6
8.2
6%
.
•87%
of
the o
bserv
ations a
re w
ithin
1.2
8
sta
ndard
devia
tions o
f th
e m
ean.
(In
a n
orm
al
dis
trib
ution p
erc
enta
ge is 8
0%
.)
Busin
ess S
tatistics: A
First C
ours
e, 5e ©
2009 P
rentice-H
all,
Inc..
Chap 6
-42
Evalu
ating N
orm
alit
yA
n E
xam
ple
: M
utu
al F
unds R
etu
rns
40
30
20
10
0-10
99.99
99
95
80
50
20 5 1
0.01
Return 2006
Percent
Probability Plot of Return 2006
Normal
(co
ntin
ue
d)
Plo
t is
appro
xim
ate
ly
a s
traig
ht
line e
xcept
for
a few
outlie
rs a
t th
e low
en
d a
nd t
he
hig
h e
nd.
Busin
ess S
tatistics: A
First C
ours
e, 5e ©
2009 P
rentice-H
all,
Inc..
Chap 6
-43
Evalu
ating N
orm
alit
yA
n E
xam
ple
: M
utu
al F
unds R
etu
rns
�C
on
clu
sio
ns
�T
he r
etu
rns a
re s
lightly left
-skew
ed
�T
he r
etu
rns h
ave m
ore
valu
es c
on
centr
ate
d a
round
the m
ean than e
xp
ecte
d
�T
he r
ange is larg
er
than e
xpecte
d (
caused b
y o
ne
outlie
r at
35.0
)
�N
orm
al pro
bab
ility
plo
t is
reasona
bly
str
aig
ht
line
�O
vera
ll, t
his
data
set does n
ot
gre
atly d
iffe
r fr
om
the
theore
tica
l pro
pert
ies o
f th
e n
orm
al d
istr
ibution(c
on
tin
ue
d)
Busin
ess S
tatistics: A
First C
ours
e, 5e ©
2009 P
rentice-H
all,
Inc..
Chap 6
-44
Cha
pte
r S
um
mary
�P
rese
nte
d n
orm
al d
istr
ibu
tio
n
�F
ou
nd
pro
ba
bili
tie
s f
or
the
no
rma
l d
istr
ibu
tio
n
�A
pp
lied
no
rma
l d
istr
ibu
tio
n t
o p
rob
lem
s
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