Chapter 7
Sampling and Sampling
Distributions
Solutions:
15.
a.
$45,500
/
$4,550
10
i
x
x
n
= Σ
=
=
b.
2
(
)
9,068,620
$1003.80
1
10
1
i
x
x
s
n
Σ

=
=
=


16.
a.
We would use the sample proportion for the estimate.
5
.10
50
p
=
=
(Authors' note: The actual proportion from New York is
52
.104.
500
p
=
=
)
b.
The sample proportion from Minnesota is
2
.04
50
p
=
=
Our estimate of the number of Fortune 500 companies from New
York is (.04)500 = 20.
(Authors' note: The actual number from Minnesota is 18.)
c.
Fourteen of the 50 in the sample come from these 4 states. So 36 do
not.
36
.72
50
p
=
=
(Authors' note: The actual proportion from the other states is
366
.732.
500
p
=
=
)
18. a.
E x
( )
=
=
μ
200
b.
σ
σ
x
n
=
=
=
/
/
50
100
5
c.
Normal with
E
(
x
)
=
200 and
σ
x
=
5
d.
It shows the probability distribution of all possible sample means
that can be observed with random samples of size 100.
This
distribution can be used to compute the probability that
x
is within
a specified
±
from
μ
.
19.
a.
The sampling distribution is normal with
E
( )
x
=
μ
= 200
/
50 /
100
5
x
n
σ
σ
=
=
=
For
±
5,
195
205
x
≤
≤
Using Standard Normal Probability Table:
At
x
= 205,
5
1
5
x
x
z
μ
σ

=
=
=
(
1)
P z
≤
= .8413
At
x
= 195,
5
1
5
x
x
z
μ
σ


=
=
= 
(
1)
P z
< 
= .1587
(195
205)
P
x
≤
≤
= .8413  .1587 = .6826
b.
For
±
10,
190
210
x
≤
≤
Using Standard Normal Probability Table:
At
x
= 210,
z
x
x
=

=
=
μ
σ
10
5
2
(
2)
P z
≤
= .9772
At
x
= 190,
10
2
5
x
x
z
μ
σ


=
=
= 
(
2)
P z
< 
= .0228
(190
210)
P
x
≤
≤
= .9772  .0228 = .9544
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Chapter 7
26.
a.
939
/
x
z
n
σ

=
Within
±
25 means
x
 939 must be between 25 and +25.
The
z
value for
x
 939 = 25 is just the negative of the
z
value for
x
 939 = 25.
So we just show the computation of
z
for
x
 939 =
25.
n
= 30
25
.56
245/
30
z
=
=
P
(.56
≤
z
.56) = .7123  .2877 = .4246
≤
n
= 50
25
.72
245/
50
z
=
=
P
(.72
≤
z
.72) = .7642  .2358 = .5284
≤
n
= 100
25
1.02
245/
100
z
=
=
P
(1.02
≤
z
1.02) = .8461  .1539 = .6922
≤
n
= 400
25
2.04
245/
400
z
=
=
P
(2.04
≤
z
2.04) = .9793  .0207 = .9586
≤
b.
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 Fall '10
 oba
 Statistics, Normal Distribution, Probability, Standard Error, σp, Z=

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