Chapter 12
12.1 a
n
/
s
t
x
2
/
α
±
= 510
±
2.064(125/
25
) = 510
±
51.60; LCL = 458.40, UCL = 561.60
b
n
/
s
t
x
2
/
α
±
= 510
±
2.009(125/
50
) = 510
±
35.51; LCL = 474.49, UCL = 545.51
c
n
/
s
t
x
2
/
α
±
= 510
±
1.984(125/
100
) = 510
±
24.80; LCL = 485.20, UCL = 534.80
d. The interval narrows.
12.2 a
n
/
s
t
x
2
/
α
±
= 1,500
±
1.984(300/
100
) = 1,500
±
59.52; LCL = 1,440.48, UCL = 1,559.52
b
n
/
s
t
x
2
/
α
±
= 1,500
±
1.984(200/
100
) = 1,500
±
39.68; LCL = 1,460.32, UCL = 1,539.68
c
n
/
s
t
x
2
/
α
±
= 1,500
±
1.984(100/
100
) = 1,500
±
19.84; LCL = 1,480.16, UCL = 1,519.84
d. The interval narrows.
12.3 a
n
/
s
t
x
2
/
α
±
= 700
±
1.645(100/
400
) = 700
±
8.23; LCL = 691.77, UCL = 708.23
b
n
/
s
t
x
2
/
α
±
= 700
±
1.96(100/
400
) = 700
±
9.80; LCL = 690.20, UCL = 709.80
a
n
/
s
t
x
2
/
α
±
= 700
±
2.576(100/
400
) = 700
±
12.88; LCL = 687.12, UCL = 712.88
d. The interval widens.
12.4 a
n
/
s
t
x
2
/
α
±
= 10
±
1.984(1/
100
) = 10
±
.20; LCL = 9.80, UCL = 10.20
b
n
/
s
t
x
2
/
α
±
= 10
±
1.984(4/
100
) = 10
±
.79; LCL = 9.21, UCL = 10.79
c
n
/
s
t
x
2
/
α
±
= 10
±
1.984(10/
100
) = 10
±
1.98; LCL = 8.02, UCL = 11.98
d The interval widens.
12.5 a
n
/
s
t
x
2
/
α
±
= 120
±
2.009(15/
51
) = 120
±
4.22; LCL = 115.78, UCL = 124.22
b
n
/
s
t
x
2
/
α
±
= 120
±
1.676(15/
51
) = 120
±
3.52; LCL = 116.48, UCL = 123.52
c
n
/
s
t
x
2
/
α
±
= 120
±
1.299(15/
51
) = 120
±
2.73; LCL = 117.27, UCL = 122.73
d The interval narrows.
12.6 a
n
/
s
t
x
2
/
α
±
= 63
±
1.990(8/
81
) = 63
±
1.77; LCL = 61.23, UCL = 64.77
b
n
/
s
t
x
2
/
α
±
= 63
±
2.000(8/
64
) = 63
±
2.00; LCL = 61.00, UCL = 65.00
c
n
/
s
t
x
2
/
α
±
= 63
±
2.030(8/
36
) = 63
±
2.71; LCL = 60.29, UCL = 65.71
251