Self help Examples with transformations from the Z distribution
 
No.
 Example Values Answer
1
 P(Y < 7.91) = ___ n = 40, Mean = 9, Var = 1 P value = 0.1379
2
 P(Y < 621.82) = ___ n = 44, Mean = 613, Var = 324 P value = 0.6879
3
 P(Y < 22.92) = ___ n = 3, Mean = 29, Var = 16 P value = 0.0643
4
 P(Y < 35.04) = ___ n = 66, Mean = 44, Var = 16 P value = 0.0125
5
 P(Y < 1083.94) = ___ n = 39, Mean = 1078, Var = 81 P value = 0.7454
6
 P(Y < 27.36) = ___ n = 29, Mean = 26, Var = 16 P value = 0.6331
7
 P(Y < 505.29) = ___ n = 97, Mean = 450, Var = 361 P value = 0.9982
8
 P(Y < 22.88) = ___ n = 82, Mean = 24, Var = 16 P value = 0.3897
9
 P(Y < 22.18) = ___ n = 67, Mean = 16, Var = 9 P value = 0.9803
10
 P(Y < 1.39) = ___ n = 85, Mean = 3, Var = 1 P value = 0.0537
11
 P(Y < 243.26) = ___ n = 16, Mean = 256, Var = 169 P value = 0.1635
12
 P(Y < 6.91) = ___ n = 12, Mean = 7, Var = 1 P value = 0.4641
13
 P(Y < 15.16) = ___ n = 78, Mean = 10, Var = 4 P value = 0.9951
14
 P(Y < 12.21) = ___ n = 95, Mean = 15, Var = 1 P value = 0.0026
15
 P(Y < 16.93) = ___ n = 79, Mean = 17, Var = 1 P value = 0.4721
16
 P(Y > 17.48) = ___ n = 78, Mean = 17, Var = 9 P value = 0.4364
17
 P(Y > 158.64) = ___ n = 12, Mean = 182, Var = 64 P value = 0.9982
18
 P(Y > 8.4) = ___ n = 52, Mean = 10, Var = 4 P value = 0.7881
19
 P(Y > 450.02) = ___ n = 76, Mean = 452, Var = 4 P value = 0.8389
20
 P(Y > 54.49) = ___ n = 9, Mean = 52, Var = 9 P value = 0.2033
21
 P(Y > 3.21) = ___ n = 48, Mean = 3, Var = 1 P value = 0.4168
22
 P(Y > -0.78) = ___ n = 62, Mean = 5, Var = 4 P value = 0.9981
23
 P(Y > 86) = ___ n = 36, Mean = 79, Var = 49 P value = 0.1587
24
 P(Y > 50.84) = ___ n = 7, Mean = 47, Var = 36 P value = 0.2611
25
 P(Y > 8.03) = ___ n = 28, Mean = 7, Var = 1 P value = 0.1515
26
 P(Y > 104.98) = ___ n = 87, Mean = 112, Var = 81 P value = 0.7823
27
 P(Y > 323.56) = ___ n = 57, Mean = 329, Var = 256 P value = 0.6331
28
 P(Y > 646.8) = ___ n = 74, Mean = 627, Var = 144 P value = 0.0495
29
 P(Y > 230.13) = ___ n = 82, Mean = 225, Var = 81 P value = 0.2843
30
 P(Y > 29.14) = ___ n = 37, Mean = 25, Var = 4 P value = 0.0192
31
 P(Y < Yo) = 0.0031 n = 31, Mean = 8, Var = 4 Yo = 2.52
32
 P(Y < Yo) = 0.992 n = 91, Mean = 11, Var = 4 Yo = 15.82
33
 P(Y < Yo) = 0.8159 n = 28, Mean = 187, Var = 169 Yo = 198.7
34
 P(Y < Yo) = 0.9842 n = 23, Mean = 572, Var = 441 Yo = 617.15
35
 P(Y < Yo) = 0.4443 n = 48, Mean = 236, Var = 169 Yo = 234.18
36
 P(Y < Yo) = 0.9965 n = 32, Mean = 11, Var = 9 Yo = 19.1
37
 P(Y < Yo) = 0.9922 n = 10, Mean = 32, Var = 16 Yo = 41.68
38
 P(Y < Yo) = 0.6141 n = 28, Mean = 18, Var = 4 Yo = 18.58
39
 P(Y < Yo) = 0.0668 n = 78, Mean = 706, Var = 484 Yo = 673
40
 P(Y < Yo) = 0.0838 n = 43, Mean = 6, Var = 1 Yo = 4.62
41
 P(Y < Yo) = 0.3632 n = 50, Mean = 7, Var = 1 Yo = 6.65
42
 P(Y < Yo) = 0.4641 n = 22, Mean = 616, Var = 529 Yo = 613.93
43
 P(Y < Yo) = 0.004 n = 78, Mean = 92, Var = 81 Yo = 68.15
44
 P(Y < Yo) = 0.9984 n = 47, Mean = 19, Var = 9 Yo = 27.85
45
 P(Y < Yo) = 0.1401 n = 61, Mean = 770, Var = 169 Yo = 755.96
46
 P(Y > Yo) = 0.758 n = 63, Mean = 9, Var = 4 Yo = 7.6
47
 P(Y > Yo) = 0.2981 n = 11, Mean = 857, Var = 529 Yo = 869.19
48
 P(Y > Yo) = 0.5398 n = 29, Mean = 5, Var = 1 Yo = 4.9
49
 P(Y > Yo) = 0.5279 n = 74, Mean = 6, Var = 4 Yo = 5.86
50
 P(Y > Yo) = 0.1762 n = 41, Mean = 199, Var = 64 Yo = 206.44
51
 P(Y > Yo) = 0.0287 n = 83, Mean = 6, Var = 4 Yo = 9.8
52
 P(Y > Yo) = 0.4129 n = 88, Mean = 19, Var = 16 Yo = 19.88
53
 P(Y > Yo) = 0.9505 n = 9, Mean = 760, Var = 324 Yo = 730.3
54
 P(Y > Yo) = 0.5793 n = 63, Mean = 29, Var = 1 Yo = 28.8
55
 P(Y > Yo) = 0.0028 n = 21, Mean = 10, Var = 4 Yo = 15.54
56
 P(Y > Yo) = 0.2946 n = 82, Mean = 32, Var = 25 Yo = 34.7
57
 P(Y > Yo) = 0.9901 n = 35, Mean = 131, Var = 64 Yo = 112.36
58
 P(Y > Yo) = 0.0475 n = 65, Mean = 165, Var = 64 Yo = 178.36
59
 P(Y > Yo) = 0.9976 n = 25, Mean = 43, Var = 16 Yo = 31.72
60
 P(Y > Yo) = 0.0485 n = 12, Mean = 1, Var = 1 Yo = 2.66
61
 P(Yo < Y) = 0.1562 n = 22, Mean = 81, Var = 25 Yo = 86.05
62
 P(Yo < Y) = 0.0618 n = 37, Mean = 767, Var = 729 Yo = 808.58
63
 P(Yo < Y) = 0.7019 n = 93, Mean = 68, Var = 4 Yo = 66.94
64
 P(Yo < Y) = 0.0174 n = 93, Mean = 8, Var = 1 Yo = 10.11
65
 P(Yo < Y) = 0.2451 n = 41, Mean = 403, Var = 196 Yo = 412.66
66
 P(Yo < Y) = 0.1736 n = 30, Mean = 304, Var = 121 Yo = 314.34
67
 P(Yo < Y) = 0.0192 n = 90, Mean = 27, Var = 9 Yo = 33.21
68
 P(Yo < Y) = 0.9893 n = 45, Mean = 33, Var = 25 Yo = 21.5
69
 P(Yo < Y) = 0.0222 n = 31, Mean = 234, Var = 4 Yo = 238.02
70
 P(Yo < Y) = 0.0136 n = 16, Mean = 9, Var = 1 Yo = 11.21
71
 P(Yo < Y) = 0.0885 n = 67, Mean = 162, Var = 25 Yo = 168.75
72
 P(Yo < Y) = 0.9898 n = 34, Mean = 7, Var = 4 Yo = 2.36
73
 P(Yo < Y) = 0.9857 n = 87, Mean = 17, Var = 9 Yo = 10.43
74
 P(Yo < Y) = 0.1977 n = 83, Mean = 646, Var = 144 Yo = 656.2
75
 P(Yo < Y) = 0.6772 n = 93, Mean = 137, Var = 64 Yo = 133.32
76
 P(Yo > Y) = 0.9934 n = 20, Mean = 8, Var = 4 Yo = 12.96
77
 P(Yo > Y) = 0.0078 n = 60, Mean = 5, Var = 4 Yo = 0.16
78
 P(Yo > Y) = 0.7642 n = 30, Mean = 7, Var = 1 Yo = 7.72
79
 P(Yo > Y) = 0.0026 n = 49, Mean = 463, Var = 324 Yo = 412.78
80
 P(Yo > Y) = 0.0066 n = 43, Mean = 32, Var = 25 Yo = 19.6
81
 P(Yo > Y) = 0.8508 n = 16, Mean = 489, Var = 441 Yo = 510.84
82
 P(Yo > Y) = 0.7088 n = 73, Mean = 2, Var = 1 Yo = 2.55
83
 P(Yo > Y) = 0.9441 n = 91, Mean = 8, Var = 1 Yo = 9.59
84
 P(Yo > Y) = 0.9641 n = 24, Mean = 10, Var = 1 Yo = 11.8
85
 P(Yo > Y) = 0.9573 n = 58, Mean = 19, Var = 9 Yo = 24.16
86
 P(Yo > Y) = 0.0045 n = 86, Mean = 3, Var = 1 Yo = 0.39
87
 P(Yo > Y) = 0.1151 n = 17, Mean = 77, Var = 64 Yo = 67.4
88
 P(Yo > Y) = 0.0024 n = 58, Mean = 30, Var = 4 Yo = 24.36
89
 P(Yo > Y) = 0.9251 n = 8, Mean = 260, Var = 169 Yo = 278.72
90
 P(Yo > Y) = 0.0869 n = 85, Mean = 31, Var = 16 Yo = 25.56
91
 P(Y1 < Z < Y2) = -0.4911 n = 29, Mean = 8, Var = 4 Y1 = 3.26, Y2 = 12.74
92
 P(Y1 < Z < Y2) = -0.334 n = 56, Mean = 34, Var = 1 Y1 = 33.03, Y2 = 34.97
93
 P(Y1 < Z < Y2) = -0.2088 n = 33, Mean = 306, Var = 196 Y1 = 298.3, Y2 = 313.7
94
 P(Y1 < Z < Y2) = -0.2257 n = 7, Mean = 28, Var = 9 Y1 = 26.2, Y2 = 29.8
95
 P(Y1 < Z < Y2) = -0.2995 n = 13, Mean = 9, Var = 4 Y1 = 7.32, Y2 = 10.68
96
 P(Y1 < Z < Y2) = -0.1591 n = 83, Mean = 205, Var = 144 Y1 = 200.08, Y2 = 209.92
97
 P(Y1 < Z < Y2) = -0.0359 n = 77, Mean = 9, Var = 1 Y1 = 8.91, Y2 = 9.09
98
 P(Y1 < Z < Y2) = -0.0517 n = 7, Mean = 51, Var = 4 Y1 = 50.74, Y2 = 51.26
99
 P(Y1 < Z < Y2) = -0.4726 n = 42, Mean = 5, Var = 1 Y1 = 3.08, Y2 = 6.92
100
 P(Y1 < Z < Y2) = -0.3238 n = 20, Mean = 10, Var = 4 Y1 = 8.14, Y2 = 11.86
101
 P(Y1 < Z < Y2) = -0.4545 n = 10, Mean = 124, Var = 100 Y1 = 107.1, Y2 = 140.9
102
 P(Y1 < Z < Y2) = -0.3869 n = 38, Mean = 3, Var = 1 Y1 = 1.79, Y2 = 4.21
103
 P(Y1 < Z < Y2) = -0.1406 n = 92, Mean = 351, Var = 225 Y1 = 345.6, Y2 = 356.4
104
 P(Y1 < Z < Y2) = -0.4959 n = 73, Mean = 21, Var = 9 Y1 = 13.08, Y2 = 28.92
105
 P(Y1 < Z < Y2) = -0.4147 n = 36, Mean = 30, Var = 4 Y1 = 27.26, Y2 = 32.74
106
 P(32.88 < Y < 41.6) = ___ n = 43, Mean = 26, Var = 16 P value = 0.0427
107
 P(13.9 < Y < 16.58) = ___ n = 51, Mean = 16, Var = 4 P value = 0.4672
108
 P(152.44 < Y < 177.4) = ___ n = 4, Mean = 159, Var = 64 P value = 0.7832
109
 P(443.98 < Y < 550.19) = ___ n = 19, Mean = 493, Var = 361 P value = 0.9938
110
 P(7.38 < Y < 9) = ___ n = 54, Mean = 9, Var = 1 P value = 0.4474
111
 P(13.48 < Y < 14.1) = ___ n = 44, Mean = 11, Var = 1 P value = 0.0056
112
 P(3.18 < Y < 6.79) = ___ n = 27, Mean = 3, Var = 1 P value = 0.4285
113
 P(546.1 < Y < 552.25) = ___ n = 9, Mean = 508, Var = 225 P value = 0.004
114
 P(259.96 < Y < 300.4) = ___ n = 46, Mean = 280, Var = 144 P value = 0.908
115
 P(882.4 < Y < 1013.68) = ___ n = 56, Mean = 952, Var = 576 P value = 0.993
116
 P(6.18 < Y < 7.17) = ___ n = 34, Mean = 6, Var = 1 P value = 0.3076
117
 P(44.52 < Y < 48.12) = ___ n = 90, Mean = 54, Var = 16 P value = 0.0619
118
 P(47.92 < Y < 50.48) = ___ n = 15, Mean = 37, Var = 16 P value = 0.0028
119
 P(53.09 < Y < 57.77) = ___ n = 82, Mean = 47, Var = 9 P value = 0.021
120
 P(32.06 < Y < 66.5) = ___ n = 47, Mean = 47, Var = 36 P value = 0.993
121
 P(Yo < Y < 32.96) = 0.2711 n = 15, Mean = 31, Var = 16 Yo = 30.16
122
 P(Yo < Y < 84.75) = 0.0985 n = 56, Mean = 65, Var = 25 Yo = 71.45
123
 P(Yo < Y < 95.32) = 0.0163 n = 59, Mean = 86, Var = 16 Yo = 93.76
124
 P(Yo < Y < 804.7) = 0.9462 n = 95, Mean = 766, Var = 100 Yo = 749.9
125
 P(Yo < Y < 28.65) = 0.0064 n = 97, Mean = 18, Var = 9 Yo = 25.44
126
 P(Yo < Y < 22.73) = 0.0187 n = 97, Mean = 11, Var = 9 Yo = 17.24
127
 P(Yo < Y < 7.56) = 0.5846 n = 53, Mean = 6, Var = 4 Yo = 4.3
128
 P(Yo < Y < 17.47) = 0.3189 n = 24, Mean = 14, Var = 1 Yo = 14.47
129
 P(Yo < Y < 1015.7) = 0.0039 n = 2, Mean = 982, Var = 100 Yo = 1008.3
130
 P(Yo < Y < 36.76) = 0.9798 n = 63, Mean = 29, Var = 4 Yo = 24.9
131
 P(Yo < Y < 390.8) = 0.3116 n = 60, Mean = 338, Var = 256 Yo = 345.84
132
 P(Yo < Y < 25.6) = 0.3332 n = 87, Mean = 22, Var = 9 Yo = 22.39
133
 P(Yo < Y < 83.48) = 0.0614 n = 50, Mean = 70, Var = 16 Yo = 76.16
134
 P(Yo < Y < 20.02) = 0.9603 n = 61, Mean = 14, Var = 4 Yo = 10.46
135
 P(Yo < Y < 374.12) = 0.0659 n = 51, Mean = 392, Var = 144 Yo = 357.92
136
 P(17.54 < Y < Yo) = 0.0028 n = 57, Mean = 12, Var = 4 Yo = 19.96
137
 P(373.88 < Y < Yo) = 0.8011 n = 42, Mean = 389, Var = 144 Yo = 404.72
138
 P(303.3 < Y < Yo) = 0.6316 n = 82, Mean = 333, Var = 100 Yo = 336.4
139
 P(680.76 < Y < Yo) = 0.0011 n = 45, Mean = 641, Var = 196 Yo = 683.84
140
 P(346.12 < Y < Yo) = 0.0049 n = 73, Mean = 305, Var = 256 Yo = 363.08
141
 P(850.8 < Y < Yo) = 0.9931 n = 93, Mean = 925, Var = 784 Yo = 1002.28
142
 P(57.32 < Y < Yo) = 0.7061 n = 17, Mean = 59, Var = 4 Yo = 61.64
143
 P(46.28 < Y < Yo) = 0.0392 n = 58, Mean = 41, Var = 9 Yo = 52.67
144
 P(58.45 < Y < Yo) = 0.2784 n = 53, Mean = 61, Var = 9 Yo = 60.82
145
 P(6.24 < Y < Yo) = 0.041 n = 45, Mean = 5, Var = 4 Yo = 6.5
146
 P(32.56 < Y < Yo) = 0.237 n = 12, Mean = 31, Var = 16 Yo = 35.88
147
 P(47.35 < Y < Yo) = 0.006 n = 71, Mean = 35, Var = 25 Yo = 50.8
148
 P(444.56 < Y < Yo) = 0.6244 n = 37, Mean = 491, Var = 324 Yo = 496.94
149
 P(12.48 < Y < Yo) = 0.0407 n = 80, Mean = 9, Var = 4 Yo = 16.1
150
 P(9.92 < Y < Yo) = 0.2638 n = 28, Mean = 12, Var = 4 Yo = 11.56
151
 P(Ybar < 199.76) = ___ n = 81, Mean = 198, Var = 36 P value = 0.9959
152
 P(Ybar < 10.25) = ___ n = 91, Mean = 10, Var = 1 P value = 0.9922
153
 P(Ybar < 22.75) = ___ n = 6, Mean = 18, Var = 16 P value = 0.9982
154
 P(Ybar < 21.41) = ___ n = 65, Mean = 21, Var = 16 P value = 0.7939
155
 P(Ybar < 69.34) = ___ n = 96, Mean = 69, Var = 36 P value = 0.7088
156
 P(Ybar < 11.69) = ___ n = 78, Mean = 12, Var = 4 P value = 0.0869
157
 P(Ybar < 84.18) = ___ n = 79, Mean = 84, Var = 9 P value = 0.7054
158
 P(Ybar < 5.72) = ___ n = 12, Mean = 6, Var = 1 P value = 0.1685
159
 P(Ybar < 14.95) = ___ n = 10, Mean = 14, Var = 1 P value = 0.9986
160
 P(Ybar < 9.63) = ___ n = 84, Mean = 10, Var = 9 P value = 0.1292
161
 P(Ybar < 10.11) = ___ n = 14, Mean = 11, Var = 4 P value = 0.0475
162
 P(Ybar < 9.11) = ___ n = 21, Mean = 9, Var = 4 P value = 0.5987
163
 P(Ybar < 7.57) = ___ n = 10, Mean = 9, Var = 4 P value = 0.0119
164
 P(Ybar < 360.05) = ___ n = 53, Mean = 363, Var = 256 P value = 0.0901
165
 P(Ybar < 29.83) = ___ n = 53, Mean = 29, Var = 16 P value = 0.9345
166
 P(Ybar > 26.13) = ___ n = 79, Mean = 26, Var = 9 P value = 0.352
167
 P(Ybar > 27.71) = ___ n = 32, Mean = 29, Var = 9 P value = 0.9927
168
 P(Ybar > 79.31) = ___ n = 79, Mean = 78, Var = 25 P value = 0.0102
169
 P(Ybar > 13.91) = ___ n = 34, Mean = 15, Var = 9 P value = 0.983
170
 P(Ybar > 59.64) = ___ n = 85, Mean = 60, Var = 4 P value = 0.9515
171
 P(Ybar > 40.4) = ___ n = 71, Mean = 42, Var = 25 P value = 0.9964
172
 P(Ybar > 629.99) = ___ n = 76, Mean = 627, Var = 81 P value = 0.0019
173
 P(Ybar > 11.19) = ___ n = 30, Mean = 11, Var = 4 P value = 0.305
174
 P(Ybar > 51.68) = ___ n = 80, Mean = 53, Var = 16 P value = 0.9985
175
 P(Ybar > 101.74) = ___ n = 10, Mean = 98, Var = 49 P value = 0.0455
176
 P(Ybar > 22.88) = ___ n = 38, Mean = 24, Var = 16 P value = 0.9582
177
 P(Ybar > 8.51) = ___ n = 37, Mean = 9, Var = 1 P value = 0.9986
178
 P(Ybar > 999.1) = ___ n = 88, Mean = 997, Var = 729 P value = 0.2327
179
 P(Ybar > 7.36) = ___ n = 17, Mean = 8, Var = 4 P value = 0.9049
180
 P(Ybar > 3.57) = ___ n = 9, Mean = 4, Var = 1 P value = 0.9032
181
 P(Ybar < Yo) = 0.4364 n = 12, Mean = 5, Var = 1 Yo = 4.9538
182
 P(Ybar < Yo) = 0.7967 n = 77, Mean = 418, Var = 256 Yo = 419.5134
183
 P(Ybar < Yo) = 0.0239 n = 17, Mean = 390, Var = 256 Yo = 382.3165
184
 P(Ybar < Yo) = 0.9177 n = 84, Mean = 63, Var = 25 Yo = 63.7583
185
 P(Ybar < Yo) = 0.2514 n = 85, Mean = 118, Var = 36 Yo = 117.564
186
 P(Ybar < Yo) = 0.0087 n = 91, Mean = 641, Var = 225 Yo = 637.2576
187
 P(Ybar < Yo) = 0.0643 n = 85, Mean = 32, Var = 16 Yo = 31.3405
188
 P(Ybar < Yo) = 0.9573 n = 88, Mean = 678, Var = 361 Yo = 681.4837
189
 P(Ybar < Yo) = 0.9554 n = 52, Mean = 94, Var = 49 Yo = 95.6502
190
 P(Ybar < Yo) = 0.0033 n = 30, Mean = 389, Var = 144 Yo = 383.0408
191
 P(Ybar < Yo) = 0.4681 n = 58, Mean = 13, Var = 4 Yo = 12.979
192
 P(Ybar < Yo) = 0.9798 n = 100, Mean = 6, Var = 1 Yo = 6.205
193
 P(Ybar < Yo) = 0.9582 n = 67, Mean = 10, Var = 4 Yo = 10.4227
194
 P(Ybar < Yo) = 0.6591 n = 87, Mean = 7, Var = 4 Yo = 7.0879
195
 P(Ybar < Yo) = 0.9744 n = 46, Mean = 5, Var = 4 Yo = 5.575
196
 P(Ybar > Yo) = 0.9972 n = 91, Mean = 479, Var = 81 Yo = 476.3866
197
 P(Ybar > Yo) = 0.9251 n = 59, Mean = 13, Var = 9 Yo = 12.4376
198
 P(Ybar > Yo) = 0.9948 n = 88, Mean = 36, Var = 16 Yo = 34.9084
199
 P(Ybar > Yo) = 0.8461 n = 40, Mean = 671, Var = 576 Yo = 667.1294
200
 P(Ybar > Yo) = 0.0023 n = 42, Mean = 9, Var = 4 Yo = 9.8764
201
 P(Ybar > Yo) = 0.0037 n = 75, Mean = 721, Var = 484 Yo = 727.8081
202
 P(Ybar > Yo) = 0.9115 n = 5, Mean = 571, Var = 400 Yo = 558.9252
203
 P(Ybar > Yo) = 0.9941 n = 100, Mean = 5, Var = 4 Yo = 4.496
204
 P(Ybar > Yo) = 0.4721 n = 28, Mean = 426, Var = 16 Yo = 426.0529
205
 P(Ybar > Yo) = 0.0985 n = 75, Mean = 28, Var = 9 Yo = 28.4469
206
 P(Ybar > Yo) = 0.8869 n = 82, Mean = 66, Var = 36 Yo = 65.1983
207
 P(Ybar > Yo) = 0.166 n = 32, Mean = 888, Var = 441 Yo = 891.6009
208
 P(Ybar > Yo) = 0.9535 n = 22, Mean = 30, Var = 16 Yo = 28.5673
209
 P(Ybar > Yo) = 0.0094 n = 11, Mean = 132, Var = 25 Yo = 135.5428
210
 P(Ybar > Yo) = 0.7054 n = 86, Mean = 53, Var = 4 Yo = 52.8835
211
 P(Yo < Ybar) = 0.9429 n = 95, Mean = 107, Var = 16 Yo = 106.3516
212
 P(Yo < Ybar) = 0.6255 n = 31, Mean = 23, Var = 16 Yo = 22.7701
213
 P(Yo < Ybar) = 0.9887 n = 19, Mean = 56, Var = 16 Yo = 53.9077
214
 P(Yo < Ybar) = 0.9599 n = 90, Mean = 49, Var = 1 Yo = 48.8155
215
 P(Yo < Ybar) = 0.997 n = 28, Mean = 981, Var = 529 Yo = 969.0469
216
 P(Yo < Ybar) = 0.3372 n = 45, Mean = 7, Var = 4 Yo = 7.1252
217
 P(Yo < Ybar) = 0.992 n = 61, Mean = 567, Var = 1 Yo = 566.6914
218
 P(Yo < Ybar) = 0.0166 n = 99, Mean = 39, Var = 25 Yo = 40.0704
219
 P(Yo < Ybar) = 0.8051 n = 21, Mean = 481, Var = 289 Yo = 477.8097
220
 P(Yo < Ybar) = 0.9981 n = 13, Mean = 10, Var = 9 Yo = 7.5871
221
 P(Yo < Ybar) = 0.591 n = 6, Mean = 6, Var = 1 Yo = 5.9061
222
 P(Yo < Ybar) = 0.0132 n = 99, Mean = 839, Var = 484 Yo = 843.9086
223
 P(Yo < Ybar) = 0.9956 n = 31, Mean = 8, Var = 4 Yo = 7.0589
224
 P(Yo < Ybar) = 0.0582 n = 68, Mean = 1042, Var = 900 Yo = 1047.7117
225
 P(Yo < Ybar) = 0.7611 n = 83, Mean = 23, Var = 16 Yo = 22.6883
226
 P(Yo > Ybar) = 0.7852 n = 72, Mean = 11, Var = 1 Yo = 11.0931
227
 P(Yo > Ybar) = 0.0146 n = 12, Mean = 1062, Var = 441 Yo = 1048.7845
228
 P(Yo > Ybar) = 0.1271 n = 89, Mean = 111, Var = 100 Yo = 109.7916
229
 P(Yo > Ybar) = 0.0392 n = 71, Mean = 551, Var = 225 Yo = 547.8669
230
 P(Yo > Ybar) = 0.0985 n = 44, Mean = 9, Var = 4 Yo = 8.6111
231
 P(Yo > Ybar) = 0.281 n = 77, Mean = 12, Var = 4 Yo = 11.8678
232
 P(Yo > Ybar) = 0.9857 n = 81, Mean = 4, Var = 4 Yo = 4.4867
233
 P(Yo > Ybar) = 0.5636 n = 48, Mean = 246, Var = 49 Yo = 246.1617
234
 P(Yo > Ybar) = 0.1894 n = 40, Mean = 6, Var = 4 Yo = 5.7217
235
 P(Yo > Ybar) = 0.2451 n = 34, Mean = 20, Var = 9 Yo = 19.645
236
 P(Yo > Ybar) = 0.8212 n = 95, Mean = 917, Var = 676 Yo = 919.4541
237
 P(Yo > Ybar) = 0.695 n = 77, Mean = 12, Var = 4 Yo = 12.1162
238
 P(Yo > Ybar) = 0.4129 n = 69, Mean = 126, Var = 100 Yo = 125.7352
239
 P(Yo > Ybar) = 0.9957 n = 26, Mean = 158, Var = 100 Yo = 163.1579
240
 P(Yo > Ybar) = 0.6293 n = 25, Mean = 768, Var = 144 Yo = 768.792
241
 P(Y1 < Ybar < Y2) = 0.9912 n = 73, Mean = 35, Var = 4 Y1 = 34.39, Y2 = 35.61
242
 P(Y1 < Ybar < Y2) = 0.9164 n = 71, Mean = 7, Var = 1 Y1 = 6.79, Y2 = 7.21
243
 P(Y1 < Ybar < Y2) = 0.9357 n = 24, Mean = 4, Var = 1 Y1 = 3.62, Y2 = 4.38
244
 P(Y1 < Ybar < Y2) = 0.9892 n = 86, Mean = 251, Var = 225 Y1 = 246.88, Y2 = 255.12
245
 P(Y1 < Ybar < Y2) = 0.766 n = 34, Mean = 56, Var = 36 Y1 = 54.78, Y2 = 57.22
246
 P(Y1 < Ybar < Y2) = 0.4177 n = 69, Mean = 9, Var = 1 Y1 = 8.93, Y2 = 9.07
247
 P(Y1 < Ybar < Y2) = 0.9876 n = 25, Mean = 324, Var = 100 Y1 = 319, Y2 = 329
248
 P(Y1 < Ybar < Y2) = 0.3108 n = 18, Mean = 436, Var = 144 Y1 = 434.87, Y2 = 437.13
249
 P(Y1 < Ybar < Y2) = 0.9857 n = 2, Mean = 40, Var = 16 Y1 = 33.07, Y2 = 46.93
250
 P(Y1 < Ybar < Y2) = 0.9707 n = 24, Mean = 14, Var = 1 Y1 = 13.56, Y2 = 14.44
251
 P(Y1 < Ybar < Y2) = 0.0558 n = 21, Mean = 11, Var = 9 Y1 = 10.95, Y2 = 11.05
252
 P(Y1 < Ybar < Y2) = 0.6579 n = 81, Mean = 2, Var = 1 Y1 = 1.89, Y2 = 2.11
253
 P(Y1 < Ybar < Y2) = 0.9586 n = 59, Mean = 179, Var = 121 Y1 = 176.08, Y2 = 181.92
254
 P(Y1 < Ybar < Y2) = 0.4448 n = 93, Mean = 438, Var = 144 Y1 = 437.27, Y2 = 438.73
255
 P(Y1 < Ybar < Y2) = 0.8904 n = 74, Mean = 43, Var = 9 Y1 = 42.44, Y2 = 43.56
256
 P(3.09 < Ybar < 3.53) = ___ n = 47, Mean = 3, Var = 1 P value = 0.2741
257
 P(422.96 < Ybar < 425.23) = ___ n = 61, Mean = 424, Var = 81 P value = 0.6736
258
 P(810.45 < Ybar < 851.38) = ___ n = 7, Mean = 826, Var = 289 P value = 0.9922
259
 P(660.42 < Ybar < 664.08) = ___ n = 94, Mean = 654, Var = 625 P value = 0.0063
260
 P(142.62 < Ybar < 143.11) = ___ n = 49, Mean = 142, Var = 49 P value = 0.1341
261
 P(95.83 < Ybar < 96.42) = ___ n = 95, Mean = 98, Var = 64 P value = 0.0227
262
 P(857.82 < Ybar < 859.3) = ___ n = 70, Mean = 853, Var = 324 P value = 0.0109
263
 P(197.23 < Ybar < 205.59) = ___ n = 20, Mean = 200, Var = 49 P value = 0.9615
264
 P(21.49 < Ybar < 21.63) = ___ n = 82, Mean = 21, Var = 4 P value = 0.011
265
 P(270.24 < Ybar < 273) = ___ n = 14, Mean = 272, Var = 121 P value = 0.3588
266
 P(13.54 < Ybar < 13.57) = ___ n = 99, Mean = 13, Var = 4 P value = 0.0011
267
 P(56.41 < Ybar < 57.33) = ___ n = 49, Mean = 56, Var = 16 P value = 0.2287
268
 P(10.71 < Ybar < 11.28) = ___ n = 13, Mean = 10, Var = 4 P value = 0.0898
269
 P(6.47 < Ybar < 8.18) = ___ n = 4, Mean = 7, Var = 1 P value = 0.8463
270
 P(129.5 < Ybar < 132.57) = ___ n = 71, Mean = 131, Var = 121 P value = 0.7599
271
 P(Yo < Ybar < 234.72) = 0.7 n = 1, Mean = 218, Var = 121 Yo = 210.08
272
 P(Yo < Ybar < 9.37) = 0.0294 n = 25, Mean = 9, Var = 1 Yo = 9.31
273
 P(Yo < Ybar < 391.24) = 0.0307 n = 94, Mean = 384, Var = 324 Yo = 387.47
274
 P(Yo < Ybar < 30.07) = 0.0364 n = 80, Mean = 29, Var = 16 Yo = 29.76
275
 P(Yo < Ybar < 6.28) = 0.0017 n = 89, Mean = 6, Var = 1 Yo = 6.26
276
 P(Yo < Ybar < 282.05) = 0.5201 n = 19, Mean = 282, Var = 4 Yo = 281.05
277
 P(Yo < Ybar < 35.79) = 0.0265 n = 92, Mean = 34, Var = 25 Yo = 35.01
278
 P(Yo < Ybar < 924.5) = 0.001 n = 43, Mean = 917, Var = 225 Yo = 923.77
279
 P(Yo < Ybar < 439.16) = 0.2603 n = 78, Mean = 435, Var = 324 Yo = 436.18
280
 P(Yo < Ybar < 196.98) = 0.1435 n = 50, Mean = 192, Var = 169 Yo = 193.93
281
 P(Yo < Ybar < 26.82) = 0.694 n = 91, Mean = 26, Var = 16 Yo = 25.76
282
 P(Yo < Ybar < 15.48) = 0.216 n = 33, Mean = 15, Var = 9 Yo = 15.14
283
 P(Yo < Ybar < 28.4) = 0.0402 n = 40, Mean = 27, Var = 9 Yo = 27.82
284
 P(Yo < Ybar < 24.26) = 0.2229 n = 57, Mean = 23, Var = 9 Yo = 23.3
285
 P(Yo < Ybar < 977.91) = 0.0016 n = 75, Mean = 973, Var = 144 Yo = 977.03
286
 P(16.31 < Ybar < Yo) = 0.1021 n = 27, Mean = 18, Var = 9 Yo = 17.27
287
 P(330.4 < Ybar < Yo) = 0.9861 n = 63, Mean = 334, Var = 144 Yo = 337.87
288
 P(3.82 < Ybar < Yo) = 0.864 n = 89, Mean = 4, Var = 1 Yo = 4.14
289
 P(5.06 < Ybar < Yo) = 0.0414 n = 62, Mean = 5, Var = 1 Yo = 5.08
290
 P(4.33 < Ybar < Yo) = 0.0049 n = 62, Mean = 4, Var = 1 Yo = 4.44
291
 P(36.03 < Ybar < Yo) = 0.4711 n = 14, Mean = 38, Var = 16 Yo = 38.01
292
 P(935.02 < Ybar < Yo) = 0.3173 n = 60, Mean = 938, Var = 484 Yo = 937.74
293
 P(83.32 < Ybar < Yo) = 0.0068 n = 28, Mean = 81, Var = 25 Yo = 84.18
294
 P(4.04 < Ybar < Yo) = 0.7964 n = 1, Mean = 6, Var = 4 Yo = 9.5
295
 P(7.29 < Ybar < Yo) = 0.034 n = 24, Mean = 8, Var = 4 Yo = 7.41
296
 P(9.18 < Ybar < Yo) = 0.0185 n = 10, Mean = 10, Var = 4 Yo = 9.25
297
 P(65.95 < Ybar < Yo) = 0.0254 n = 7, Mean = 63, Var = 16 Yo = 68.46
298
 P(10.74 < Ybar < Yo) = 0.0023 n = 53, Mean = 10, Var = 4 Yo = 10.84
299
 P(424.46 < Ybar < Yo) = 0.9866 n = 30, Mean = 433, Var = 400 Yo = 442.75
300
 P(8.73 < Ybar < Yo) = 0.0051 n = 45, Mean = 8, Var = 4 Yo = 8.85

 

Revised March 19, 2002
James P. Geaghan