have a length of life that is approximately normally distributed with a standard deviation of 50 hours. If a sample of 45 bulbs has an average life of 790 hours, find a 96% confidence interval for the population mean of all bulbs produced by this firm. The confidence interval is ________ < μ < ____________
have a length of life that is approximately normally distributed with a standard deviation of 50 hours. If a sample of 45 bulbs has an average life of 790 hours, find a 96% confidence interval for the population mean of all bulbs produced by this firm. The confidence interval is ________ < μ < ____________
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.2: Representing Data
Problem 24PFA
Related questions
Question
100%
An electrical firm manufactures light bulbs that have a length of life that is approximately
The confidence interval is ________ < μ < ____________
Transcribed Image Text:الها
Areas under the Normal Curve
> >
2
.00
Areas under the Normal Curve
.01
.02
.03
.04
0.0129
0.4443
.01
.02
.04
z
.00
.01
.02
.03
.04
.05
.06
.07
-3.4 0.0003 0.0003 0.0003 0.0003 0.0003 0.0003 0.0003 0.0003
-3.3 0.0005 0.0005 0.0005 0.0004 0.0004 0.0004 0.0004 0.0004
-3.2 0.0007 0.0007 0.0006 0.0006 0.0006 0.0006 0.0006 0.0005
0.0010 0.0009
-3.1
0.0009 0.0009 0.0008 0.0008 0.0008
-3.0 0.0013 0.0013 0.0013 0.0012 0.0012 0.0011 0.0011
-2.9 0.0019 0.0018 0.0018 0.0017 0.0016 0.0016 0.0015
-2.8 0.0026 0.0025 0.0024 0.0023 0.0023 0.0022 0.0021
-2.7 0.0035 0.0034 0.0033 0.0032 0.0031
0.0030 0.0029 0.0028 0.0027 0.0026 -2.7
-2.6
0.0047 0.0045 0.0044 0.0043 0.0041 0.0040 0.0039 0.0038 0.0037 0.0036 -2.6
-2.5 0.0062 0.0060 0.0059 0.0057 0.0055 0.0054 0.0052 0.0051 0.0049 0.0048 -2.5
-2.4 0.0082
0.0078 0.0075
0.0080
0.0073 0.0071 0.0069 0.0068 0.0066 0.0064 -2.4
-2.3 0.0107 0.0104 0.0102 0.0099 0.0096 0.0094 0.0091 0.0089 0.0087 0.0084 -2.3
-2.2 0.0139 0.0136 0.0132
0.0125 0.0122 0.0119 0.0116 0.0113 0.0110 -2.2
-2.1 0.0179 0.0174 0.0170 0.0166
0.0162 0.0158 0.0154 0.0150 0.0146 0.0143 -2.1
-2.0 0.0228 0.0222 0.0217 0.0212 0.0207 0.0202 0.0197 0.0192 0.0188 0.0183 -2.0
-1.9
0.0281
0.0287
0.0268
0.0274
0.0262 0.0256 0.0250
0.0239
0.0244
0.0233 -1.9
-1.8 0.0359 0.0351 0.0344 0.0336 0.0329 0.0322 0.0314 0.0307 0.0301 0.0294 -1.8
-1.7
0.0436 0.0427 0.0418
0.0446
0.0409 0.0401
0.0384 0.0375 0.0367
0.0392
-1.7
-1.6 0.0548 0.0537 0.0526 0.0516 0.0505 0.0495 0.0485 0.0475 0.0465 0.0455 -1.6
-1.5 0.0668 0.0655 0.0643 0.0630 0.0618 0.0606 0.0594 0.0582 0.0571 0.0559 -1.5
-1.4 0.0808 0.0793 0.0778 0.0764 0.0749 0.0735 0.0721 0.0708 0.0694 0.0681 -1.4
-1.3 0.0968 0.0951
0.0918 0.0901 0.0885
0.0934
0.0869 0.0853 0.0838 0.0823 -1.3
-1.2 0.1151 0.1131 0.1112 0.1093 0.1075 0.1056 0.1038 0.1020 0.1003 0.0985
-1.2
-1.1 0.1357 0.1335 0.1314 0.1292 0.1271 0.1251 0.1230 0.1210
0.1190
-1.1
0.1170
-1.0
0.1587 0.1562 0.1539 0.1515 0.1492 0.1469 0.1446 0.1423 0.1401 0.1379 -1.0
0.1841
0.1788 0.1762
0.1814
0.1736 0.1711 0.1685 0.1660
-0.9
0.1611 -0.9
0.1635
-0.8 0.2119
0.2061 0.2033 0.2005
0.2090
0.1977 0.1949 0.1922 0.1894
-0.8
0.1867
-0.7 0.2420 0.2389 0.2358 0.2327 0.2296 0.2266 0.2236 0.2206 0.2177 0.2148 -0.7
-0.6 0.2743 0.2709 0.2676 0.2643 0.2611 0.2578 0.2546 0.2514 0.2483 0.2451 -0.6
-0.5 0.3085 0.3050 0.3015 0.2981 0.2946 0.2912 0.2877 0.2843 0.2810 0.2776 -0.5
-0.4 0.3446 0.3409 0.3372 0.3336 0.3300 0.3264 0.3228 0.3192 0.3156 0.3121 -0.4
-0.3 0.3821 0.3783 0.3745 0.3707 0.3669 0.3632 0.3594 0.3557 0.3520 0.3483 -0.3
-0.2 0.4207
0.4090
0.4013
0.3974
0.4168
0.3897
0.4129
0.3859 -0.2
0.4052
0.3936
0.4602
0.4483
-0.1
0.4562
0.4364
0.4522
0.4325 0.4286
0.4404
-0.1
0.4247
-0.0 0.5000 0.4960 0.4920 0.4880 0.4840 0.4801 0.4761 0.4721 0.4681 0.4641 -0.0
.00
.03
.05
.06
.07
.08
.08
.09
2
0.0003 0.0002 -3.4
0.0004 0.0003 -3.3
0.0005 0.0005 -3.2
0.0008 0.0007 0.0007 -3.1
0.0011 0.0010 0.0010 -3.0
0.0015 0.0014
0.3
0.0021 0.0020
0.0014 -2.9
0.0019 -2.8
1.6
1.7
1.8
1.9
2.1
1
+
2.9 0.9981
3.0
3.1
.07
0.0 0.5000 0.5040 0.5080 0.5120 0.5160 0.5199 0.5239 0.5279 0.5319
0.1 0.5398 0.5438 0.5478 0.5517 0.5557 0.5596 0.5636 0.5675 0.5714
0.2 0.5793 0.5832 0.5871 0.5910 0.5948 0.5987 0.6026 0.6064 0.6103
0.6179 0.6217 0.6255 0.6293 0.6331 0.6368 0.6406 0.6443 0.6480 0.6517 0.3
0.4 0.6554 0.6591 0.6628 0.6664 0.6700 0.6736 0.6772 0.6808 0.6844 0.6879 0.4
0.5 0.6915 0.6950 0.6985 0.7019 0.7054 0.7088 0.7123 0.7157 0.7190 0.7224 0.5
0.6 0.7257 0.7291 0.7324 0.7357 0.7389 0.7422 0.7454 0.7486 0.7517 0.7549 0.6
0.7 0.7580 0.7611 0.7642 0.7673 0.7704 0.7734 0.7764 0.7794 0.7823 0.7852 0.7
0.8 0.7881
0.7910 0.7939 0.7967 0.7995 0.8023 0.8051 0.8078 0.8106 0.8133 0.8
0.9 0.8159
0.8186 0.8212 0.8238 0.8264 0.8289 0.8315 0.8340 0.8365 0.8389 0.9
1.0 0.8413 0.8438 0.8461 0.8485 0.8508 0.8531 0.8554 0.8577 0.8599 0.8621 1.0
0.8643
1.1
0.8665 0.8686 0.8708
0.8749
0.8729
0.8770 0.8790 0.8810
1.1
0.8830
1.2 0.8849 0.8869 0.8888 0.8907 0.8925 0.8944 0.8962 0.8980 0.8997 0.9015 1.2
1.3 0.9032 0.9049 0.9066 0.9082 0.9099 0.9115 0.9131 0.9147 0.9162 0.9177 1.3
1.4 0.9192 0.9207 0.9222 0.9236 0.9251 0.9265 0.9279 0.9292 0.9306 0.9319 1.4
1.5 0.9332 0.9345 0.9357 0.9370 0.9382 0.9394 0.9406 0.9418 0.9429 0.9441 1.5
0.9463
0.9452
0.9474 0.9484 0.9495 0.9505 0.9515
1.6
0.9525 0.9535 0.9545
0.9554 0.9564 0.9573 0.9582 0.9591 0.9599 0.9608 0.9616 0.9625 0.9633 1.7
0.9649 0.9656
0.9641
0.9664 0.9671
0.9693
0.9678 0.9686
0.9706
0.9699
1.8
0.9713 0.9719 0.9726 0.9732 0.9738 0.9744 0.9750 0.9756 0.9761 0.9767 1.9
2.0 0.9772 0.9778 0.9783 0.9788 0.9793 0.9798 0.9803 0.9808 0.9812 0.9817 2.0
0.9821 0.9826 0.9830 0.9834 0.9838 0.9842 0.9846 0.9850 0.9854 0.9857 2.1
2.2 0.9861 0.9864 0.9868 0.9871 0.9875 0.9878 0.9881 0.9884 0.9887 0.9890 2.2
2.3 0.9893 0.9896 0.9898 0.9901 0.9904 0.9906 0.9909 0.9911
0.9913 0.9916 2.3
2.4 0.9918 0.9920 0.9922 0.9925 0.9927 0.9929 0.9931 0.9932 0.9934 0.9936 2.4
2.5 0.9938 0.9940 0.9941 0.9943 0.9945 0.9946 0.9948 0.9949 0.9951 0.9952 2.5
2.6 0.9953 0.9955 0.9956 0.9957 0.9959 0.9960 0.9961
0.9963 0.9964
0.9962
2.6
0.9965
2.7
0.9966 0.9967 0.9968
0.9970
0.9969
0.9971 0.9972 0.9973 0.9974 2.7
回 2.8 0.9974 0.9975 0.9976 0.9977 0.9977 0.9978 0.9979 0.9979 0.9980 0.9981 2.8
0.9982 0.9982 0.9983 0.9984 0.9984 0.9985
0.9987 0.9987 0.9987 0.9988 0.9988 0.9989 0.9989
0.9990 0.9991
.05
.06
.08
.09
0.5359 0.0
0.5753 0.1
0.6141 0.2
0.9985 0.9986 0.9986 2.9
A
3.2
3.3
A 3.4
0.9991 0.9991 0.9992 0.9992 0.9992
0.9993 0.9993 0.9994 0.9994 0.9994 0.9994 0.9994 0.9995 0.9995 0.9995 3.2
0.9989 0.9990 0.9990 3.0
0.9992 0.9993 0.9993 3.1
2
0.9995 0.9995
0.9997 0.9997
.00
.01
0.9995 0.9996
0.9997 0.9997
.02
.03
0.9996
0.9996
0.9997
0.9997
0.9996
0.9997
.04
.05
.06
0.9996 0.9996
0.9997 0.9997
.07
.08
0.9997
0.9998
.09
3.3
3.4
.09
2
Transcribed Image Text:Critical Values of the t-Distribution
> >
☑=
Critical Values of the t-Distribution
a
a
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
14.089
31.600
2
0.289
0.617
1.061
1.386
1.886
2.920
4.303
3
3.482
3.896
4.541
5.047
5.841
7.453
12.924
3
0.277
0.584
0.978
1.250
1.638
2.353
3.182
4
2.999
3.298
3.747
4.088
4.604
5.598
8.610
4
0.271
0,569
0.941
1.190
1.533
2.132
2.776
5
2.757
3.003
3.365
3.634
4.032
4.773
6.869
5
0.267
0.559
0.920
1.156
1.476
2.015
2.571
6
2.612
2.829
3.143
3.372
3.707
4.317
5.959
6
0.265
0.553
0.906
1.134
1.440
1.943
2.447
7
2.517
2.715
2.998
3.203
3.499
4.029
5.408
7
0.263
0.549
0.896
1.119
1.415
1.895
2.365
8
2.449
2.634
2.896
3.085
3.355
3.833
5.041
8
0.262
0.546
0.889
1.108
1.397
1.860
2.306
9
2.398
2.574
2.821
2.998
3.250
3.690
4.781
9
0.261
0.543
0.883
1.100
1.383
1.833
2.262
2.359
2.527
2.764
2.932
3.169
3.581
4.587
10
0.260
0.542
0.879
1.093
1.372
1.812
2.228
2.328
2.491
2.718
2.879
3.106
3.497
4.437
11
0.260
0.540
0.876
1.088
1.363
1.796
2.201
2.303
2.461
2.681
2.836
3.055
3.428
4.318
12
0.259
0.539
0.873
1.083
1.356
1.782
2.179
2.282
2.436
2.650
2.801
3.012
3.372
4.221
13
0.259
0.538
0.870
1.079
1.350
1.771
2.160
2.264
2.415
2.624
2.771
2.977
3.326
4.140
14
0.258
0.537
0.868
1.076
1.345
1.761
2.145
2.249
2.397
2.602
2.746
2.947
3.286
4.073
15
0.258
0.536
0.866
1.074
1.341
1.753
2.131
2.235
2.382
2.583
2.724
2.921
3.252
4.015
16
0.258
0.535
0.865
1.071
1.337
1.746
2.120
2.224
2.368
2.567
2.706
2.898
3.222
3.965
17
0.257
0.534
0.863
1.069
1.333
1.740
2.110
2.214
2.356
2.552
2.689
2.878
3.197
3.922
18
0.257
0.534
0.862
1.067
1.330
1.734
2.101
2.205
2.346
2.539
2.674
2.861
3.174
3.883
19
0.257
0.533
0.861
1.066
1.328
1.729
2.093
2.197
2.336
2.528
2.661
2.845
3.153
3.850
20
0.257
0.533
0.860
1.064
1.325
1.725
2.086
2.189
2.328
2.518
2.649
2.831
3.135
3.819
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
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
28
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
ت
30
0.256
0.530
0.854
1.055
1.310
1.697
2.042
125%
40
0.255
0.529
0.851
1.050
1.303
1.684
2.021
60
0.254
0.527
0.848
1.045
1.296
1.671
2.000
120
120
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
88 888 888-
2.183
2.320
2.508
2.639
2.819
3.119
3.792
2.177
2.313
2.500
2.629
2.807
3.104
3.768
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
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
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
"
0.40
0.30
0.20
0.15
0.10
0.05
0.025
a
Q
a
Ο
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