A random sample of 100 automobile owners in a region shows that an automobile is driven on average 22 comma 000 kilometers per year with a standard deviation of 4500 kilometers. Assume the distribution of measurements to be approximately normal. Construct a 95% prediction interval for the kilometers traveled annually by an automobile owner in the region. The prediction interval is ______< Xo < _____ (Round to the nearest integer as needed.)
A random sample of 100 automobile owners in a region shows that an automobile is driven on average 22 comma 000 kilometers per year with a standard deviation of 4500 kilometers. Assume the distribution of measurements to be approximately normal. Construct a 95% prediction interval for the kilometers traveled annually by an automobile owner in the region. The prediction interval is ______< Xo < _____ (Round to the nearest integer as needed.)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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Question
A random sample of 100 automobile owners in a region shows that an automobile is driven on average 22 comma 000 kilometers per year with a standard deviation of 4500 kilometers. Assume the distribution of measurements to be approximately normal. Construct a 95% prediction interval for the kilometers traveled annually by an automobile owner in the region.
The prediction interval is ______< Xo < _____
(Round to the nearest integer as needed.)
Transcribed Image Text:Areas under the Normal Curve
Areas under the Normal Curve
z
.00
.01
-3.4
0.0003 0.0003 0.0003 0.0003
-3.3 0.0005 0.0005 0.0005 0.0004
-3.2 0.0007 0.0007 0.0006 0.0006
-3.1 0.0010 0.0009 0.0009 0.0009
-3.0 0.0013 0.0013 0.0013 0.0012
-2.9 0.0019 0.0018 0.0018 0.0017
-2.8 0.0026 0.0025 0.0024 0.0023
-2.7 0.0035 0.0034 0.0033 0.0032
-2.6 0.0047 0.0045 0.0044 0.0043
-2.5 0.0062 0.0060 0.0059 0.0057
-2.4 0.0082 0.0080 0.0078 0.0075
-2.3 0.0107 0.0104 0.0102 0.0099
.02
.03
.05
.04
.06
.07
0.0003 0.0003
0.0003 0.0003
0.0004 0.0004 0.0004 0.0004
0.0006 0.0006 0.0006 0.0005
0.0008 0.0008 0.0008 0.0008
0.0012 0.0011 0.0011 0.0011
0.0016 0.0016 0.0015 0.0015
0.0023 0.0022 0.0021 0.0021
0.0031 0.0030 0.0029 0.0028
.08
.09
0.0003 0.0002 -3.4
0.0004 0.0003 -3.3
0.0005 0.0005 -3.2
z
Z
.00
.01
.02
.03
.04
.05
.06
.07
0.0007 0.0007 -3.1
0.0010 0.0010 -3.0
0.3
0.4
-0.3 0.3821 0.3783 0.3745
2
.00
.01
0.0041 0.0040 0.0039 0.0038
0.0055 0.0054 0.0052 0.0051
0.0073 0.0071 0.0069 0.0068 0.0066 0.0064 -2.4
0.0096 0.0094 0.0091 0.0089 0.0087
-2.2 0.0139 0.0136 0.0132 0.0129 0.0125 0.0122 0.0119 0.0116 0.0113
-2.1 0.0179 0.0174 0.0170 0.0166 0.0162 0.0158 0.0154 0.0150 0.0146
-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 0.0287 0.0281 0.0274 0.0268 0.0262 0.0256 0.0250 0.0244 0.0239 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 0.0446 0.0436 0.0427 0.0418 0.0409 0.0401 0.0392 0.0384 0.0375 0.0367 -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 0.0934 0.0918 0.0901 0.0885 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 0.1170 -1.1
-1.0 0.1587 0.1562 0.1539 0.1515 0.1492 0.1469 0.1446 0.1423 0.1401 0.1379 -1.0
-0.9 0.1841 0.1814 0.1788 0.1762 0.1736 0.1711 0.1685 0.1660 0.1635 0.1611 -0.9
-0.8 0.2119 0.2090 0.2061 0.2033 0.2005 0.1977 0.1949 0.1922 0.1894 0.1867 -0.8
-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
-0.5 0.3085 0.3050 0.3015 0.2981 0.2946 0.2912 0.2877 0.2843
-0.4 0.3446 0.3409 0.3372 0.3336 0.3300 0.3264 0.3228 0.3192
0.3707 0.3669 0.3632 0.3594 0.3557
0.3483 -0.3
-0.2 0.4207 0.4168 0.4129 0.4090 0.4052 0.4013 0.3974 0.3936 0.3897 0.3859 -0.2
-0.1 0.4602 0.4562 0.4522 0.4483 0.4443 0.4404 0.4364 0.4325 0.4286 0.4247 -0.1
-0.0 0.5000 0.4960 0.4920 0.4880 0.4840 0.4801 0.4761 0.4721 0.4681 0.4641 -0.0
.02
.03
.04
.05
.06
.07
.08
.09
Z
0.0014 0.0014 -2.9
0.0020 0.0019 -2.8
0.0027 0.0026 2.7
0.0037 0.0036 -2.6
0.0049 0.0048 -2.5
0.5
0.0084 -2.3
0.0110 -2.2
0.0143 -2.1
2.7
0.2483 0.2451 -0.6
0.2810
0.2776 -0.5
0.3156
0.3520
0.3121 -0.4
¡A
2
.00
0.0 0.5000 0.5040 0.5080 0.5120 0.5160 0.5199 0.5239 0.5279
0.1 0.5398 0.5438 0.5478 0.5517 0.5557 0.5596 0.5636 0.5675 0.5714 0.5753 0.1
0.2 0.5793 0.5832 0.5871 0.5910 0.5948 0.5987 0.6026 0.6064 0.6103 0.6141 0.2
0.6179 0.6217 0.6255
0.6293 0.6331
0.6368 0.6406 0.6443 0.6480 0.6517 0.3
0.6554 0.6591 0.6628 0.6664 0.6700 0.6736 0.6772 0.6808 0.6844 0.6879 0.4
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
1.1 0.8643 0.8665 0.8686 0.8708 0.8729 0.8749 0.8770 0.8790 0.8810 0.8830 1.1
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
1.6 0.9452 0.9463 0.9474 0.9484 0.9495 0.9505 0.9515 0.9525 0.9535 0.9545 1.6
1.7 0.9554 0.9564 0.9573 0.9582 0.9591 0.9599 0.9608 0.9616 0.9625 0.9633 1.7
1.8 0.9641 0.9649 0.9656 0.9664 0.9671 0.9678 0.9686 0.9693 0.9699 0.9706 1.8
1.9 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
2.1 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 0.9962 0.9963 0.9964 2.6
0.9965 0.9966 0.9967
0.9968 0.9969 0.9970 0.9971 0.9972 0.9973 0.9974 2.7
2.8
0.9974 0.9975 0.9976 0.9977 0.9977 0.9978 0.9979 0.9979 0.9980 0.9981 2.8
2.9 0.9981 0.9982 0.9982 0.9983 0.9984 0.9984 0.9985 0.9985 0.9986 0.9986 2.9
3.0 0.9987 0.9987 0.9987 0.9988 0.9988 0.9989 0.9989 0.9989 0.9990 0.9990 3.0
3.1 0.9990 0.9991 0.9991 0.9991 0.9992 0.9992
0.9992 0.9992 0.9993 0.9993 3.1
3.2 0.9993
0.9993 0.9994 0.9994 0.9994 0.9994 0.9994 0.9995 0.9995 0.9995 3.2
3.3 0.9995 0.9995 0.9995 0.9996 0.9996 0.9996 0.9996 0.9996 0.9996 0.9997 3.3
3.4 0.9997 0.9997 0.9997 0.9997 0.9997 0.9997 0.9997 0.9997 0.9997 0.9998 3.4
.01
.02
.03
.04
.05
.06
.07
.08
.09
.08
.09
0.5319 0.5359 0.0
2
Z
Transcribed Image Text:Critical Values of the Chi-Squared Distribution
Q
25
0.995
0.99
1 0.04393 0.03157 0.03628
0.98
0.975
0.03982
0.80
2 0.0100 0.0201 0.0404 0.0506
0.103
3 0.0717 0.115
0.185
0.216
0.352
0.584
0.95
0.75
0.90
0.70 0.50
0.00393 0.0158 0.0642 0.102 0.148 0.455
0.211 0.446 0.575 0.713 1.386
1.005 1.213 1.424 2.366
4 0.207
0.297
0.429
0.484
0.711
1.064
1.649
1.923 2.195 3.357
5 0.412
0.554
0.752
0.831
1.145
1.610
2.343
2.675 3.000 4.351
6 0.676
0.872
1.134
1.237
1.635
2.204
3.070
3.455 3.828 5.348
7 0.989
1.239 1.564
1.690
2.167
2.833 3.822
4.255 4.671 6.346
8
1.344
1.647
2.032
2.180
2.733
3.490
4.594
5.071 5.527 7.344
9 1.735
2.088
2.532
2.700
3.325
4.168
10 2.156
2.558
3.059
3.247
3.940
4.865
5.380
6.179
5.899 6.393 8.343
6.737 7.267 9.342
11 12.899
11
2.603
3.053 3.609
3.816
4.575
12 3.074
3.571
4.178
4.404
5.226
13
3.565
4.107
4.765
5.009 5.892
14 4.075
4.660
5.368
5.629
6.571
5.578 6.989
6.304 7.807
7.041 8.634
7.790 9.467
12 14.011
7.584 8.148 10.341
8.438 9.034 11.340
14 16.222
9.299 9.926 12.340
15 17.322
10.165 10.821 13.339
15
4.601
5.229
5.985
6.262
16
5.142
5.812
6.614
6.908
17 5.697
6.408
7.255
7.564
18 6.265
7.015
7.906
8.231
19 6.844
7.633
8.567
8.907
20
21 8.034
8.260
7.434
9.237
9.591
22 8.643
23 9.260
24 9.886
25 10.520
8.547 10.307
9.312 11.152
10.085 12.002
9.390 10.865 12.857
10.117 11.651 13.716
10.851
15.452 16.266 19.337
12.443 14.578
8.897 9.915 10.283 11.591 13.240 15.445 16.344 17.182 20.337
9.542 10.600 10.982 12.338 14.041 16.314 17.240 18.101 21.337
10.196 11.293 11.689 13.091 14.848 17.187 18.137 19.021 22.337
10.856 11.992 12.401 13.848 15.659 18.062 19.037 19.943 23.337
11.524 12.697 13.120 14.611 16.473 18.940 19.939 20.867 24.337
26 11.160 12.198 13.409 13.844 15.379 17.292 19.820 20.843 21.792 25.336
27 11.808 12.878 14.125 14.573 16.151 18.114 20.703 21.749 22.719 26.336
28 12.461 13.565 14.847 15.308 16.928 18.939 21.588 22.657 23.647 27.336
29 13.121 14.256 15.574 16.047 17.708 19.768 22.475 23.567 24.577 28.336
16.306
30 13.787 14.953
24.478 25.508 29.336
16.791 18.493 20.599 23.364
40 20.707 22.164 23.838 24.433 26.509 29.051 32.345 33.66 34.872 39.335
50 27.991 29.707 31.664 32.357 34.764 37.689 41.449 42.942 44313 49.335
60 35.534 37.485 39.699 40.482 43.188 46.459 50.641 52.294 53.809 59.335
7.261
11.037 11.721 14.339
16 18.418
17 19.511
7.962
8.672
11.912 12.624 15.338
12.792 13.531 16.338
13.675 14.440 17.338
14.562 15.352 18.338
1
1
a
A
0.995
0.99
0.98
0.975
0.95
0.90
0.80
0.75 0.70 0.50
C
0.30
0.25
1
1.074
1.323
2
2.773
в 7.231
Critical Values of the Chi-Squared Distribution
a
0.20 0.10 0.05 0.025 0.02 0.01 0.005 0.001
1.642 2.706
6.635 7.879
3.841 5.024 5.412
10.827
2.408
3.219 4.605 5.991 7.378 7.824 9.210 10.597 13.815
3 3.665 4.108 4.642 6.251 7.815 9.348 9.837 11.345 12.838 16.266
4 4.878 5.385 5.989 7.779 9.488 11.143 11.668 13.277 14.860 18.466
5 6.064 6.626 7.289
9.236 11.070 12.832 13.388 15.086 16.750 20.515
7.841 8.558 10.645 12.592 14.449 15.033 16.812 18.548 22.457
T 8.383 9.037 9.803 12.017 14.067 16.013 16.622 18.475 20.278 24.321
8 9.524 10.219 11.030 13.362 15.507 17.535 18.168 20.090 21.955 26.124
9 10.656 11.389 12.242 14.684 16.919 19.023 19.679 21.666 23.589 27.877
10 11.781 12.549 13.442 15.987 18.307 20.483 21.161 23.209 25.188 29.588
13.701 14.631 17.275 19.675 21.920 22.618 24.725 26.757 31.264
14.845 15.812 18.549 21.026 23.337 24.054 26.217 28.300 32.909
15.984 16.985 19.812 22.362 24.736 25.471 27.688 29.819 34.527
17.117 18.151 21.064 23.685 26.119 26.873 29.141 31.319 36.124
13 15.119
18.245 19.311 22.307 24.996 27.488 28.259 30.578 32.801 37.698
19.369 20.465 23.542 26.296 28.845 29.633 32.000 34.267 39.252
20.489 21.615 24.769 27.587 30.191 30.995 33.409 35.718 40.791
18 20.601 21.605 22.760 25.989 28.869 31.526 32.346 34.805 37.156 42.312
19 21.689 22.718 23.900 27.204 30.144 32.852 33.687 36.191 38.582 43.819
20 22.775 23.828 25.038 28.412 31.410 34.170 35.020 37.566 39.997 45.314
21
26.171 29.615 32.671 35.479
23.858 24.935
36.343 38.932 41.401 46.796
22 24.939 26.039 27.301 30.813 33.924 36.781 37.659 40.289 42.796 48.268
23 26.018 27.141 28.429 32.007 35.172 38.076 38.968 41.638 44.181 49.728
24 27.096 28.241 29.553 33.196 36.415 39.364 40.270 42.980 45.558 51.179
25 28.172 29.339 30.675 34.382 37.652 40.646 41.566 44.314 46.928 52.619
26 29.246 30.435 31.795 35.563 38.885 41.923 42.856 45.642 48.290 54.051
27 30.319 31.528 32.912 36.741 40.113 43.195 44.140 46.963 49.645 55.475
28 31.391 32.620 34.027 37.916 41.337 44.461 45.419 48.278 50.994 56.892
29 32.461 33.711
45.722
35.139 39.087 42.557
46.693 49.588 52.335 58.301
30 33.530 34.800 36.250 40.256 43.773 46.979 47.962 50.892 53.672 59.702
40 44.165 45.616 47.269 51.805 55.758 59.342 60.436 63.691 66.766 73.403
50 54.723 56.334 58.164 63.167 67.505 71.420 72.613 76.154 79.490 86.660
68.972 74.397 79.082 83.298 84.58 88.379 91.952 99.608
60
65.226
66.981
a
0.30
0.25
0.20
0.10
0.05
0.025 0.02
0.01 0.005 0.001
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