°±²³² ´µ
¶·¸¹º»¼½¾»¿À´
±»Á·Â¸»ÃÄ
6.13.
a.
The population from which we are randomly sampling
n
= 35 measurements is not necessarily
normally distributed. However, the sampling distribution of
x
does have an approximately normal
distribution, with mean
μ
and standard deviation
n
/
σ
.
The probability of interest is
[
]
[
]
[
]
[
]
1
)
(
1
)
(
1
)
(
1
1

<


<

=
<

<

=
<

μ
μ
μ
μ
x
P
x
P
x
P
x
P
Standardizing, we have:
[
]
[
]
[
]
[
]
°
±
²
³
´
µ

+

<

°
±
²
³
´
µ

+
<
=
+

<

+
<
=

<


<

35
/
12
)
1
(
35
/
12
)
1
(
1
1
1
)
(
1
)
(
μ
μ
μ
μ
μ
μ
μ
μ
z
P
z
P
x
P
x
P
x
P
x
P
[
]
[
]
3758
.
0
)
1879
.
0
(
2
493
.
0
493
.
0
=
=

<

<
=
z
P
z
P
where, since
σ
is unknown, we use the sample standard deviation
s
= 12 (we can do this, since the
sample size is large enough).
b.
No. There are many possible values for
x
, the actual percent tax savings, as given by the
probability distribution for
x
.
6.16.
a.
The sample mean
x
is normally distributed, since the original strength measurements are
Normally distributed, with mean
μ
and standard deviation
10
/
2
/
=
n
σ
.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
This is the end of the preview.
Sign up
to
access the rest of the document.
 Spring '08
 EduardoMontoya
 Normal Distribution, Standard Deviation, Financial aid, $30, $31,876

Click to edit the document details