Soc 375 Homework Assignment due before class on Tuesday, November 2Your name:
HELP: Read pp. 124-133 in Wonnacott and Wonnacott
There is a table of Normal deviates (“Z values”) in the inside front cover of Wonnacott and Wonnac
I have put a copy of this table under the “Content” page of our D2L website.
ANSWERS ARE AT THE BOTTOM
Batting average = (total number of hits) / (total number of official batting attempts).
In the American League in 1998, the distribution of batting averages was
approximately a Normal distribution with a mean of .268 and a standard
deviation of .031.
a) What is the probability that an American League player had a batting
average of .300 or higher? (The same question: What fraction of all
American League players had a batting average of .300 or higher?)
b) What is the probability that an American League player had a batting
average of .236 or lower?
c) What is the probability that an American League player had a batting
average between .236 and .300?
ANSWERS: (a) .152 (b) .152 also (c) .696 PLEASE SHOW YOUR WORK.
f Wonnacott and Wonnacott (repeated on p. 672)
0
Critical point. For example:
t.025 leaves .025 probability
in the tail.
V
t Critical Points
d.f. t.25 t. 10
tos
1.025
t.010
t.005
t.0025
t0010
t.0005
1
2
3
4
1.00
.82
.76
.74
3.08
1.89
1.64
1.53
6.31
2.92
2.35
2.13
12.7
4.30
3.18
2.78
31.8
6.96
4.54
3.75
63.7
9.92
5.84
4.60
127
14.1
7.45
5.60
318
22.3
10.2
7.17
637
31.6
12.9
8.61
LCON OOO
5
6
7
8
9
.73
.72
.71
.71
.70
1.48
1.44
1.41
1.40
1.38
2.02
1.94
1.89
1.86
1.83
2.57
2.45
2.36
2.31
2.26
3.36
3.14
3.00
2.90
2.82
4.03
3.71
3.50
3.36
3.25
4.77
4.32
4.03
3.83
3.69
5.89
5.21
4.79
4.50
4.30
6.87
5.96
5.41
5.04
4.78
10
11
12
13
.70
.70
.70
.69
.69
1.37
1.36
1.36
1.35
1.35
1.81
1.80
1.78
1.77
1.76
2.23
2.20
2.18
2.16
2.14
2.76
2.72
2.68
2.65
2.62
3.17
3.11
3.05
3.01
2.98
3.58
3.50
3.43
3.37
3.33
4.14
4.02
3.93
3.85
3.79
4.59
4.44
4.32
4.22
4.14
14
15
16
17
18
19
.69
.69
.69
.69
.69
1.34
1.34
1.33
1.33
1.33
1.75
1.75
1.74
1.73
1.73
2.13
2.12
2.11
2.10
2.09
2.60
2.58
2.57
2.55
2.54
2.95
2.92
2.90
2.88
2.86
3.29
3.25
3.22
3.20
3.17
3.73
3.69
3.65
3.61
3.58
4.07
4.01
3.97
3.92
3.88
20
21
22
.69
.69
.69
.69
.68
1.33
1.32
1.32
1.32
1.32
1.72
1.72
1.72
1.71
1.71
2.09
2.08
2.07
2.07
2.06
2.53
2.52
2.51
2.50
2.49
2.85
2.83
2.82
2.81
2.80
3.15
3.14
3.12
3.10
3.09
23
24
3.55
3.53
3.50
3.48
3.47
3.85
3.82
3.79
3.77
3.75
25
26
27
28
29
.68
.68
.68
.68
.68
1.32 1.71
1.31 1.71
1.31 1.70
1.31
1.70
1.31 1.70
2.06
2.06
2.05
2.05
2.05
2.49
2.48
2.47
2.47
2.46
2.79
2.78
2.77
2.76
2.76
3.08
3.07
3.06
3.05
3.04
3.45
3.43
3.42
3.41
3.40
3.73
3.71
3.69
3.67
3.66
30
40
60
120
.68
.68
.68
.68
1.31
1.30
1.30
1.29
1.70
1.68
1.67
1.66
2.04
2.02
2.00
1.98
2.46
2.42
2.39
2.36
2.75
2.70
2.66
2.62
3.03
2.97
2.92
2.86
3.39
3.31
3.23
3.16
3.65
3.55
3.46
3.37
.67
2.33
1.28
= 2.10
1.64 1.96
= 7.05 = 2.025
2.58
2.81 3.09 3.29
= 2.005 = 2.0025 = 2.0010 = 2.0005
= 7.25
= 2.010
Area = Pr (Z 220)
Ο έρ
BLE IV Standard Normal, Cumulative Probability in Right-Hand Tail
(For Negative Values of z, Areas are Found by Symmetry)
NEXT DECIMAL PLACE OF ZO
3 4
5 6
Zo
0
1
2
7
8
9
0.0
0.1
0.2
0.3
0.4
.500
.460
.421
.382
.345
.496
.456
.417
.378
.341
.492
.452
.413
.374
.337
.488
.448
.409
.371
.334
.484
.444
.405
.367
.330
.480
.440
.401
.363
.326
.476
.436
.397
.359
.323
.472
.433
.394
.356
.319
.468 .464
.429 .425
.390 .386
.352 .348
.316 .312
0.5
0.6
0.7
0.8
0.9
.309
.274
.242
.212
.184
.305
.271
.239
.209
.181
.302
.268
.236
.206
.179
.298
.264
.233
.203
.176
.295
.261
.230
.200
.174
.291
.258
.227
.198
.171
.288
.255
.224
.195
.169
.284
.251
.221
.192
.166
.281
.248
.218
.189
.164
.278
.245
.215
.187
.161
1.0
1.1
1.2
1.3
1.4
.159
.136
.115
.097
.081
.156
.133
.113
.095
.079
.154
.131
.111
.093
.078
.152
.129
.109
.092
.076
.149
.127
.107
.090
.075
.147
.125
.106
.089
.074
.145 .142
.123 .121
.104 .102
.087 085
.072 .071
.140
.119
.100
.084
.069
.138
.117
.099
.082
.068
1.5
1.6
1.7
1.8
1.9
.067
.055
.045
.036
.029
.066 064 063
.054 053 052
.044 .043
.042
.035
.034 .034
.028 .027 .027
.062
.051
.041
.033
.026
.061
.049
.040
.032
.026
.059
.048
.039
.031
.025
.058 .057
.047 .046
.038 .038
.031 .030
.024 .024
.056
.046
.037
.029
.023
2.4
2.0 .023 .022 .022 .021 .021
2.1 .018 .017 .017 .017 .016
2.2 .014 .014 .013 013 .013
2.3
.011 .010 .010 .010 .010
.008 .008 .008 .008 .007
2.5 .006 006 006 006 .006
2.6 .005 .005 004 .004 .004
2.7 .003 .003 .003 .003 .003
2.8 .003 .002.002 .002.002
2.9 .002 .002.002 .002.002
.020 .020.019.019.018
.016 .015.015 .015 .014
.012 .012 .012.011 011
.009 .009.009.009 .008
.007 .007 .007 .007 .006
.005 .005 .005 .005
.005
.004
.004 .004 .004 .004
.003 .003 .003 .003 .003
.002 .002.002 .002.002
.002 .002 .001 .001 .001
Zo
DETAIL OF TAIL (.2135, FOR EXAMPLE, MEANS .00135)
2.
3.
4.
5.
-1228 .179 .1139 .107 -2820
-2135 .3968 .3687 .3483 .3337
-4317-4207 .4133 5854 5541
.6287 .6170 .7996.,579.7333
-2621
-2466 2347 -2256 .2187
-3233 .3159 -3108 .4723 4481
-5340 5211 .5130 -6793 6479
.,190.107 .3599 -8332 8182
.8
0
1
2
3
4
5
6
7 8 9