(a) The confidence interval is ☐
Chapter8: Sequences, Series,and Probability
Section8.7: Probability
Problem 4ECP: Show that the probability of drawing a club at random from a standard deck of 52 playing cards is...
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100%
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Transcribed Image Text:(a) A random sample of 200 voters in a town is selected, and 111 are found to support an annexation suit. Find the
96% confidence interval for the fraction of the voting population favoring the suit.
(b) What can be asserted with 96% confidence about the possible size of the error if the fraction of voters favoring the
annexation suit is estimated to be 0.62?
Click here to view page 1 of the normal probability table.
Click here to view page 2 of the normal probability table.
(a) The confidence interval is ☐ <p<[
(Round to three decimal places as needed.)
(b) The possible size of the error with the given estimate is
(Round to three decimal places as needed.)
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
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