Siven a random sample of size 26 from a normal distribution, find k such that a) P(-2.060
Siven a random sample of size 26 from a normal distribution, find k such that a) P(-2.060
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter13: Probability And Calculus
Section13.3: Special Probability Density Functions
Problem 15E: Describe the standard normal distribution. What are its characteristics?
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Transcribed Image Text:Critical Values of the t-Distribution (Page 2)
U
Critical Values of the t-Distribution
P
1
2
3
4
5
6
7
8
9
10
11
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15
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19
20
21
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25
26
27
28
29
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40
0.02
15.894
4.849
3.482
2.999
2.757
2.612
2.517
2.449
2.398
2.359
2.328
2.303
2.282
2.264
2.249
2.235
2.224
2.214
2.205
2.197
2.189
2.183
2.177
2.172
2.167
2.162
2.158
2.154
2.150
2.147
2.1922
0.015
0.01
21.205 31.821
6.965
5.643
3.896
3.298
3.003
2.829
3.143
2.715 2.998
2.634
2.896
2.574
2.821
2.527
2.764
2.718
2.681
2.650
2.624
2.602
2.491
2.461
2.436
2.415
2.397
2.382
2.368
2.356
2.346
2.336
2.328
2.320
2.313
2.307
2.301
4.541
3.747
3.365
2.296
2.291
2.286
2.282
2.278
2.250
2.583
2.567
2.552
2.539
2.528
2.518
2.508
2.500
2.492
2.485
2.479
2.473
2.467
2.462
2.457
2.122
a
0.0075
42.433
8.073
5.047
4.088
3.634
3.372
3.203
3.085
2.998
2.932
2.879
2.836
2.801
2.771
2.746
2.724
2.706
2.689
2.674
2.661
2.649
2.639
2.629
2.620
2.612
2.605
2.598
2.592
2.586
2.581
22.19
0.005
63.656
9.925
5.841
4.604
4.032
3.707
3.499
3.355
3.250
3.169
3.106.
3.055
3.012
2.977
2.947
2.921
2.898
2.878
2.861
2.845
2.831
2.819
2.807
2.797
2.787
2.779
2.771
2.763
2.756
2.750
2.301
0.0025
127.321
14.089
7.453
5.598
4.773
4.317
4.029
3.833
3.690
3.581
3.497
3.428
3.372
3.326
3.286
3.252
3.222
3.197
3.174
3.153
3.135
3.119
3.104
3.091
3.078
3.067
3,957
3.17
3.038
3.030
2.071
0.0005
636.578
31.600
12.924
8.610
6.869
5,959
5.408
5.041
4.781
4.587
4.437
4.318
4.221
4.140
4.073
4.015
3.965
3.922
3.883
3.850
3.819
3.792
3.768
3.745
3.725
3.707
3.689
3.674
3.660
3,646
2.55.1
Transcribed Image Text:Given a random sample of size 26 from a normal distribution, find k such that
(a)
P(-2.060<T<k)=0.965.
(b) Find P(k <T<3.078)=0.0475.
(c) Find P(-k<T<k)=0.80.
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.)
T
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
0.40
0.325
0.289
0.277
0.271
0.267
0.265
0.263
0.262
0.261
0.260
0.260
0.259
0.259
0.258
0.258
0.258
0.257
0.257
0.257
0.257
0.257
0.256
0.256
0.256
0.256
0.256
0.256
0.30
0.727
0.617
0.584
0.569
0.559
0.553
0.549
0.546
0.543
0.542
0.540
0.539
0.538
0.537
0.536
0.535
0.534
0.534
0.533
0.533
0.532
0.532
0.532
0.531
0.531
0.531
0.531
0.20
1.376
1.061
0.978
0.941
0.920
0.906
0.896
0.889
0.883
0.879
0.876
0.873
0.870
0.868
0.866
0.865
0.863
0.862
0.861
0.860
0.859
0.858
0.858
0.857
0.856
0.856
0.855
a
0.15
1.963
1.386
1.250
1.190
1.156
1.134
1.119
1.108
1.100
1.093
1.088
1.083
1.079
1.076
1.074
1.071
1.069
1.067
1.066
1.064
1.063
1.061
1.060
1.059
1.058
1.058
1.057
0.10
3.078
1.886
1.638
1.533
1.476
1.440
1.943
1.415
1.896
1.397- 1.860
1.833
1.812
1.383
1.372
1.363
1.356
1.350
1.345
1.341
1.337
1.333
1.330
1.328
1.325
1.323
1.321
1.319
1.318
1.316
0.05
6.314
2.920
2.353
2.132
2.015
1.315
1.314
1.796
1.782
1.771
1.761
1.753
1.746
1.740
1.734
1.729
1.725
1.721
1.717
1.714
1.711
1.708
1.706
1.703
0.025
12.706
4.303
3.182
2.776
2.571
2.447
2.365
2.306
2.262
2.228
2.201
2.179
2.160
2.145
2.131
2.120
2.110
2.101
2.093
2.086
2.080
2.074
2.069
2.064
2.060
2.056
2.052
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