Given a random sample of size 22 from a normal distribution, find k such that (a) P(-1.721
Given a random sample of size 22 from a normal distribution, find k such that (a) P(-1.721
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
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I need help with this please parts a to c
Transcribed Image Text:Given a random sample of size 22 from a normal distribution, find k such that
(a) P(-1.721 <T<k) = 0.945.
(b) Find P(k<T<2.080) = 0.075.
(c) Find P(-k<T<k) = 0.98.
Click here to view page 1 of the table of critical values of the t-distribution.
Click here to view page 2 of the table of critical values of the t-distribution.
(a) k=
(Round to three decimal places as needed.)
Transcribed Image Text:Critical Values of the t-Distribution
> >
Critical Values of the t-Distribution
a
a
せ
0.02
0.015
0.01
0.0075
0.005
0.0025
0.0005
0.40
0.30
0.20
0.15
0.10
0.05
0.025
1
15.894
21.205 31.821
42.433
63.656
127.321
636.578
1
0.325
0.727
1.376
1.963
3.078
6.314
12.706
2
4.849
5.643
6.965
8.073
9.925
2
14.089
31.600
0.289
0.617
1.061
1.386
1.886
2.920
4.303
3
3.482
3.896
4.541
3
0.277
0.584
0.978
1.250
5.047
5.841
7.453
1.638
12.924
2.353
3.182
4
2.999
3.298
3.747
4.088
4.604
5.598
4
0.271
0.569
0.941
1.190
8.610
1.533
2.132
2.776
5
2.757
3.003
5
0.267
3.365
3.634
4.032
0.559
0.920
4.773
6.869
1.156
1.476
2.015
2.571
6
2.612
2.829
3.143
3.372
3.707
4.317
в
0.265
0.553
0.906
5.959
1.134
1.440
1.943
2.447
7
0.263
0.549
0.896
1.119
1.415
1.895
2.365
8
0.262
0.546
0.889
1.108
1.397
1.860
2.306
9
0.261
0.543
0.883
1.100
1.383
1.833
2.262
10
0.260
0.542
0.879
1.093
1.372
1.812
2.228
11
0.260
0.540
0.876
1.088
1.363
1.796
2.201
12
0.259
0.539
0.873
1.083
1.356
1.782
2.179
13
0.259
0.538
0.870
1.079
1.350
1.771
2.160
14
0.258
0.537
0.868
1.076
1.345
1.761
2.145
15
15
0.258
0.536
0.866
1.074
1.341
1.753
2.131
16
0.258
0.535
0.865
1.071
1.337
1.746
2.120
17
0.257
0.534
0.863
1.069
1.333
1.740
2.110
27
28
40
60
120
22 88 881
18
0.257
0.534
0.862
1.067
1.330
1.734
2.101
19
0.257
0.533
0.861
1.066
1.328
1.729
2.093
20
0.257
0.533
0.860
1.064
1.325
1.725
2.086
21
0.257
0.532
0.859
1.063
1.323
1.721
2.080
22
0.256
0.532
0.858
1.061
1.321
1.717
2.074
23
0.256
0.532
0.858
1.060
1.319
1.714
2.069
24
0.256
0.531
0.857
1.059
1.318
1.711
2.064
25
25
0.256
0.531
0.856
1.058
1.316
1.708
2.060
26
0.256
0.531
0.856
1.058
1.315
1.706
2.056
27
0.256
0.531
0.855
1.057
1.314
1.703
2.052
0.256
0.530
0.855
1.056
1.313
1.701
2.048
29
0.256
0.530
0.854
1.055
1.311
1.699
2.045
30
0.256
0.530
0.854
1.055
1.310
1.697
2.042
0.255
0.529
0.851
1.050
1.303
1.684
2.021
0.254
0.527
0.848
1.045
1.296
1.671
2.000
0.254
0.526
0.845
1.041
1.289
1.658
1.980
0.253
0.524
0.842
1.036
1.282
1.645
1.960
0.40
0.30
0.20
0.15
0.10
0.05
0.025
a
'C''
e
A
- - › U
29
30
40
60
120
TRANNAN 88 P
7
2.517
2.715
2.998
3.203
3.499
4.029
5.408
8
2.449
2.634
2.896
3.085
3.355
3.833
5.041
9
2.398
2.574
2.821
2.998
3.250
3.690
4.781
10
2.359
2.527
2.764
2.932
3.169
3.581
4.587
11
2.328
2.491
2.718
2.879
3.106
3.497
4.437
12
2.303
2.461
2.681
2.836
3.055
3.428
4.318
13
2.282
2.436
2.650
2.801
3.012
3.372
4.221
14
2.264
2.415
2.624
2.771
2.977
3.326
4.140
2.249
2.397
2.602
2.746
2.947
3.286
4.073
16
2.235
2.382
2.583
2.724
2.921
3.252
4.015
17
2.224
2.368
2.567
2.706
2.898
3.222
3.965
18
2.214
2.356
2.552
2.689
2.878
3.197
3.922
19
2.205
2.346
2.539
2.674
2.861
3.174
3.883
20
2.197
2.336
2.528
2.661
2.845
3.153
3.850
21
2.189
2.328
2.518
2.649
2.831
3.135
3.819
22
2.183
2.320
2.508
2.639
2.819
3.119
3.792
23
2.177
2.313
2.500
2.629
2.807
3.104
3.768
24
2.172
2.307
2.492
2.620
2.797
3.091
3.745
2.167
2.301
2.485
2.612
2.787
3.078
3.725
26
2.162
2.296
2.479
2.605
2.779
3.067
3.707
2.158
2.291
2.473
2.598
2.771
3.057
3.689
28
2.154
2.286
2.467
2.592
2.763
3.047
3.674
2.150
2.282
2.462
2.586
2.756
3.038
3.660
2.147
2.278
2.457
2.581
2.750
3.030
3.646
2.123
2.250
2.423
2.542
2.704
2.971
3.551
2.099
2.223
2.390
2.504
2.660
2.915
3.460
2.076
2.196
2.358
2.468
2.617
2.860
3.373
2.054
2.170
2.326
2.432
2.576
2.807
3.290
0.02
0.015
0.01
0.0075
0.005
0.0025
0.0005
a
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