A pair of dice is rolled 120 times. What is the probability that a total of 7 occurs (a) at least 17 times? (b) between 25 and 31 times inclusive? (c) exactly 20 times? Click here to view page 1 of the standard normal distribution table. Click here to view page 2 of the standard normal distribution table. (a) The probability is (Round to four decimal places as needed.) (b) The probability is (Round to four decimal places as needed.) (c) The probability is (Round to four decimal places as needed.)
A pair of dice is rolled 120 times. What is the probability that a total of 7 occurs (a) at least 17 times? (b) between 25 and 31 times inclusive? (c) exactly 20 times? Click here to view page 1 of the standard normal distribution table. Click here to view page 2 of the standard normal distribution table. (a) The probability is (Round to four decimal places as needed.) (b) The probability is (Round to four decimal places as needed.) (c) The probability is (Round to four decimal places 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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Transcribed Image Text:Areas under the Normal Curve
.08
.09
0.5319 0.5359 0.0
0.5714 0.5753 0.1
0.6103 0.6141 0.2
2
.00
.01
.02
.03
.04
.05
.06
.07
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
0.2 0.5793 0.5832 0.5871 0.5910 0.5948 0.5987 0.6026 0.6064
0.3 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
0.6915 0.6950 0.6985 0.7019 0.7054 0.7088 0.7123 0.7157 0.7190 0.7224 0.5
0.7257 0.7291 0.7324 0.7357 0.7389 0.7422 0.7454 0.7486 0.7517 0.7549 0.6
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
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
0.9948 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
2.7 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
0.9977 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
0.9975 0.9976
0.9945 0.9946
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
.00
.01
.02
.03
.04
.05
.06
.07
.08
.09
.00
Areas under the Normal Curve
Z
[=
2
-3.4
-3.3
2.
.00
.01
.04
.01
.02
.03
.04
.05
.06
.08
0.0003 0.0003 0.0003 0.0003 0.0003 0.0003 0.0003 0.0003 0.0003 0.0002 -3.4
0.0005 0.0005 0.0005 0.0004
0.0004 0.0004 0.0004 0.0004 0.0004
0.0003 -3.3
-3.2
0.0007 0.0007 0.0006 0.0006 0.0006 0.0006 0.0006 0.0005 0.0005
0.0005 -3.2
-3.1 0.0010 0.0009 0.0009 0.0009 0.0008 0.0008 0.0008 0.0008 0.0007 0.0007 -3.1
-3.0 0.0013 0.0013 0.0013 0.0012 0.0012 0.0011 0.0011 0.0011 0.0010 0.0010 -3.0
-2.9 0.0019 0.0018 0.0018 0.0017 0,0016 0.0016 0.0015 0.0015 0.0014 0.0014 -2.9
-2.8
0.0026 0.0025 0.0024 0.0023 0.0023 0.0022 0.0021 0.0021 0.0020
-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 0.0080 0.0078 0.0075 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 0.0129 0.0125 0.0122 0.0119 0.0116
-2.1 0.0179 0.0174 0.0170 0.0166 0.0162 0.0158 0.0154 0.0150
-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 0.2483 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
-0.3 0.3821 0.3783 0.3745 0.3707 0.3669 0.3632 0.3594 0.3557 0.3520
-0.2 0.4207 0.4168 0.4129 0.4090 0.4052
0.4013 0.3974 0.3936
-0.1 0.4602 0.4562 0.4522 0.4483 0.4443 0.4404 0.4364
-0.0 0.5000 0.4960 0.4920 0.4880 0.4840 0.4801 0.4761
.02
.03
.05
.07
.09
Z
0.5
0.6
0.0019 -2.8
0.7
0.0113 0.0110 -2.2
0.0146 0.0143 -2.1
1.7
1
+
1
0.3121 -0.4
0.3483 -0.3
0.3897
0.4286
.06
0.3859 -0.2
0.4325
0.4247 -0.1
0.4721 0.4681 0.4641 -0.0
.07 .08
.09
e
C
A
Z
Q
Transcribed Image Text:A pair of dice is rolled 120 times. What is the probability that a total of 7 occurs
(a) at least 17 times?
(b) between 25 and 31 times inclusive?
(c) exactly 20 times?
Click here to view page 1 of the standard normal distribution table.
Click here to view page 2 of the standard normal distribution table.
(a) The probability is ☐ .
(Round to four decimal places as needed.)
(b) The probability is
(Round to four decimal places as needed.)
(c) The probability is
(Round to four decimal places as needed.)
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