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Probability
that more than (>) 51 missiles will be off-target is cimal places inoluding any zeros.) that less than (<) 35 missiles will be off-target is U cimal places including any zeros.) that at least (2) 37 but less than (<) 49 missiles will be off-target is cimal places including any zeros.)

that more than (>) 51 missiles will be off-target is cimal places inoluding any zeros.) that less than (<) 35 missiles will be off-target is U cimal places including any zeros.) that at least (2) 37 but less than (<) 49 missiles will be off-target is cimal places including any zeros.)

A First Course in Probability (10th Edition)
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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A new military defense system is tested. It is found that 1 out of 10 missiles fired on ground objects are off-target. The system needs to be used for firing 400 missiles during a potential military attack. Apply Normal approximation to calculate the following probabilities. 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 that more than (>) 51 missiles will be off-target is- (Round to four decimal places including any zeros.) (b) The probability that less than (<) 35 missiles will be off-target is (Round to four decimal places including any zeros.) (c) The probability that at least (2) 37 but less than (<) 49 missiles will be off-target is (Round to four decimal places including any zeros.)
Transcribed Image Text:A new military defense system is tested. It is found that 1 out of 10 missiles fired on ground objects are off-target. The system needs to be used for firing 400 missiles during a potential military attack. Apply Normal approximation to calculate the following probabilities. 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 that more than (>) 51 missiles will be off-target is- (Round to four decimal places including any zeros.) (b) The probability that less than (<) 35 missiles will be off-target is (Round to four decimal places including any zeros.) (c) The probability that at least (2) 37 but less than (<) 49 missiles will be off-target is (Round to four decimal places including any zeros.)
.00 .01 .02 .03 .04 .05 .06 .07 .08 .09 .00 .01 .02 03 .04 .05 .06 .07 .08 .09 0.0 0.5000 0.5010 0.5080 0.5120 0.5160 0.5199 0.5239 0.5279 0.5319 0.5359 0.0 3.4 0.0003 0.0003 0.0003 0.0003 0.0003 0.0003 0.0003 0.0003 0.0003 0.0002 -3.4 0,5714 0.5753 0.6103 0.6141 0.6480 0.6517 0.6844 0.1 0,5398 0.5438 0.5478 0,5517 0.5557 0,5596 0,5636 0.5675 0.6064 0.1 -3.3 3.2 3.1 0.0005 0.0005 0.0005 0,0004 0,0004 0.0001 0,0004 0,0004 0.0004 0,0003 -3.3 0.2 0.5793 0.5832 0.5948 0.6026 0.6406 0.643 0.5871 0.5910 0.5987 0.2 0.0007 0.0007 0.0006 0.0006 0.0006 0.0006 0.0006 0.0005 0.0005 0.0005 -3.2 0.3 0.6179 0.6217 0.6255 0.6293 0.6331 0.63G8 0.3 -3.1 -3.0 0.0010 0.0009 0.0009 0.0009 0.0008 0.0008 0.0008 0.0008 0.0007 0.0007 -3.1 0.4 0.6554 0.6591 0.6628 0.6064 0.6700 0.6736 0.6772 0.6808 0.6879 0.4 0.0013 0.0013 0.0013 0.0012 0.0012 0.0011 0,0011 0.0011 0.0010 0.0010 -3.0 0.5 0.6 0.6950 0.7291 0.7611 0.6915 0.6985 0.7019 0.7324 0.7357 0.7642 0.7673 0.7123 0.7157 0.7454 0.7486 0.7190 0.7224 0.7517 0.7549 0.7054 0.7088 0.5 -2.9 -2.8 2.7 0.0019 0.0018 0.0018 0.0017 0.0016 0,0016 0,0015 0.0015 0.0014 0.0014 -2.9 0.7257 0.7580 0.7389 0.7422 0.7704 0.7734 0.6 0.0026 0.0025 0.0024 0.0023 0.0023 0.0022 0.0021 0.0021 0.0020 0.0019 -2.8 0.7 0.7764 0.7794 0.8051 0.8078 0.7823 0.7852 0.0028 0.0027 0.0026 -2.7 0,7 0.8 0.0035 0.0034 0.0033 0.0032 0.0031 0.0030 0.0029 0.8 0.7881 0.7910 0.7939 0.7967 0.7995 0.8023 0.8106 0.8133 -2.6 0.0047 0.0045 0.0044 0.0043 0.0011 0.0040 0.0039 0.0038 0.0037 0.0036 -2.6 0.9 0.8159 0.8186 0.8212 0.8238 0.8264 0.8289 0.8315 0.8340 0.8365 0.8389 0.9 -2.5 0.0062 0.0060 0.0059 0.0057 0.0055 0,0054 0,0052 0.0051 0.0049 0.0048 -2.5 1.0 0,8413 0.8438 0,8461 0.8485 0.8508 0.8531 0.8554 0.8577 0.8599 0.8621 0,8810 0,8830 1.0 2.4 0.0082 0.0080 0.0078 0.0075 0.0073 0.0071 0.0069 0.0068 0.0066 0.0064 2.4 0.8686 0.8708 0.8770 0.8962 0.8980 1.1 0,8643 0.8665 0.8729 0.8749 0.8790 -2.3 0.0107 -2.2 0.0139 0.0102 0.0136 0.0132 1.1 1.2 0.0104 66000 0.0096 0.0094 0.0091 0.0089 0.0087 0.0084 -2.3 1.2 0,8849 0.8869 0.8888 0,8907 0.8925 0.8944 0.8097 0.9015 0.0129 0.0125 0.0122 0.0119 0.0116 -2.2 0.0150 0.0146 0.0143 -2.1 2.0 0.0113 0.0110 1.3 0.9032 0.9019 0.9066 0.9082 0.9099 0.9115 0.9131 0.9147 0.9162 0.9177 1.3 -2.1 2.0 0.0174 0.0170 0.0222 0.0217 0.0162 0.0207 0,0179 0.0166 0.0158 0.0154 1.4 0.9192 0.9207 0.9222 0.9236 0.9251 0.9265 0.9279 0.9292 0.9306 0.9319 1.4 0.0228 0.0212 0.0202 0.0197 0.0192 0.0188 0.0183 1.5 0.9332 0.9452 0.9554 0.9345 0.9357 0,9370 0.9382 0.9394 0.9406 0.9418 0.9429 0.9441 0.9535 0.9545 0.9633 1.5 0.0281 0.0274 0.0351 0.0344 0.0256 0.020O 0.0233 -1.9 -1.9 -1.8 0.0287 0.0268 0.0336 0.0262 0.0244 0.0239 0.0301 1.6 0.9463 0.9564 0.9474 0.9484 0.9582 0.9573 0.9495 0 9589 0 9s01 0.9525 0.9616 0.9505 0.9515 1.6 0.0350 0.0329 0.0322 0.0314 0,030 0.0307 0.0204 -1.8 1.7 0.9591 0.9599 0.9608 0,9625 1.7 -1.7 -1.6 -1.5 0.0367 -1.7 0.0475 0.0465 0.0455 -1.6 0.0582 0.0571 0.0559 -1.5 0.0446 0.0436 0.0427 0.0418 0.0400 0.0401 0.0392 0.0384 0.0375 1.8 0.9641 0.9649 0.9719 0.9726 0.9732 0.9656 0,9004 0.9671 0.9678 0.9686 0.9693 0.9099 0.9706 1.8 0.0548 0.006S 0.0537 0.0526 0.0655 0.0643 0.0630 0.0516 0.0505 0.0495 0.0485 1.9 0.9713 0.9738 0.9744 0.9750 0.9756 0.9761 0.9767 1.9 0.0618 0.0606 0.0594 2.0 0.9772 0.9778 0.9783 0,9788 0.9793 0.9798 0,9803 0.9808 0,9812 0.9817 2.0 -1.4 -1.3 -1.2 0.1151 0.0808 0.0793 0.0778 0.0764 0.0749 0.0735 0.0721 0.0708 0.0694 0.0681 -1.4 0.0823 -1.3 2.1 0.9821 0.9826 0.9864 0.9868 0.9871 0.9830 0.9834 0.9838 0.9842 0,9846 0.9881 0.9850 0,9854 0.9857 2.1 0.0001 0.0885 0.0869 0.1075 0.1056 0.1038 0.1230 0.1446 0.0968 0.0961 0.0934 0.0918 0.0853 0.0838 2.2 0,9861 0.9875 0.9878 0.9884 0.9887 0.9890 2.2 0.1131 0.1112 0.1314 0.1093 0.1292 0.1020 0.1210 0.1190 0.1003 0,0085 -1.2 2.3 0,9893 0,9806 0.9898 0.9901 0.9904 0.9906 0.9909 0.9911 0.9913 0.9916 2.3 -1.1 0.1357 0.1335 0.1271 0.1251 0.1170 -1.1 2.4 0.9918 0.9920 0.9922 0.9025 0.9927 0.9029 0.9031 0.9932 0.9934 0.9936 2.4 -1.0 0.1587 0.1562 0.1539 0.1515 0.1492 0.1469 0.1423 0.1401 0.1379 -1.0 0.9951 0.9952 0.9963 0.9964 0.9973 0.9974 0.9979 0.9980 0.9981 0.9086 0.9986 2.5 0.9938 0.9910 0.9941 0.9943 0.9945 0.9946 0.9948 0.9949 2.5 0.9 0.1736 0.1711 0.1685 0.2005 0.2296 0.2266 0.2236 0.2611 0.2946 0.2912 0.2877 0.1660 0.1635 0.1922 0.2206 0.1841 0.1814 0.1788 0.1762 0.1611 0.9 2.6 0.9953 0,9955 0.9956 0.9057 0.9950 0,9060 0.9961 0.9962 2.6 0.2119 0.2420 0.2033 0.2327 0.2643 0.8 0.2000 0.2061 0.1977 0.1949 0.1894 0.1867 0.8 0.9960 0.9970 0.9977 0.9978 0.9984 0.99s4 2.7 0,9065 0.9006 0.9967 0.9968 0.9971 0.9972 2.7 2.8 0.7 -0.6 0.2743 -0.5 -0.4 0.3 0.2 0.2389 0.2709 0.2358 0.2676 0.2177 0.2514 0.2483 0.2148 0.2451 -0.7 2.8 2.9 0.9974 0.9981 0.9975 0.9976 0.9977 0.9082 0.9979 0.9985 0.2578 0.2546 -0.6 0.9982 0.9083 0.9985 2.9 0.3085 0.3050 0.3015 0.2981 0.2843 0.2810 0.2776 -0.5 3.0 0.9989 0.9087 0,9990 0.9987 0.9987 0.9988 0.9988 0.9989 0.9989 0.9990 0.9990 3.0 0.3446 0.3409 0.3372 0.3336 0.3300 0.3264 0.3228 0.3192 0.3156 0.3121 -0.4 3.1 0,9901 0.9991 0.9992 0.9991 0.9994 0.9092 0.9992 0.9992 0.9093 0.9903 3.1 0.3821 0.4207 0.4168 0.3520 0.3483 0.3897 0.3869 -0.2 0.3783 0.3745 0.3707 0.3632 0.3594 0.4090 0.40G2 0.4013 0.3974 0.3669 0.3557 -0.3 3.2 0.9993 0.9903 0.9994 0.9991 0.9994 0.9995 0 0006 0.9904 0.9996 0.9995 3.2 0.4129 0.3936 00005 0 0005 00005 00006 00006 0 0006 00006 0 00006 0 0007 33 000
Transcribed Image Text:.00 .01 .02 .03 .04 .05 .06 .07 .08 .09 .00 .01 .02 03 .04 .05 .06 .07 .08 .09 0.0 0.5000 0.5010 0.5080 0.5120 0.5160 0.5199 0.5239 0.5279 0.5319 0.5359 0.0 3.4 0.0003 0.0003 0.0003 0.0003 0.0003 0.0003 0.0003 0.0003 0.0003 0.0002 -3.4 0,5714 0.5753 0.6103 0.6141 0.6480 0.6517 0.6844 0.1 0,5398 0.5438 0.5478 0,5517 0.5557 0,5596 0,5636 0.5675 0.6064 0.1 -3.3 3.2 3.1 0.0005 0.0005 0.0005 0,0004 0,0004 0.0001 0,0004 0,0004 0.0004 0,0003 -3.3 0.2 0.5793 0.5832 0.5948 0.6026 0.6406 0.643 0.5871 0.5910 0.5987 0.2 0.0007 0.0007 0.0006 0.0006 0.0006 0.0006 0.0006 0.0005 0.0005 0.0005 -3.2 0.3 0.6179 0.6217 0.6255 0.6293 0.6331 0.63G8 0.3 -3.1 -3.0 0.0010 0.0009 0.0009 0.0009 0.0008 0.0008 0.0008 0.0008 0.0007 0.0007 -3.1 0.4 0.6554 0.6591 0.6628 0.6064 0.6700 0.6736 0.6772 0.6808 0.6879 0.4 0.0013 0.0013 0.0013 0.0012 0.0012 0.0011 0,0011 0.0011 0.0010 0.0010 -3.0 0.5 0.6 0.6950 0.7291 0.7611 0.6915 0.6985 0.7019 0.7324 0.7357 0.7642 0.7673 0.7123 0.7157 0.7454 0.7486 0.7190 0.7224 0.7517 0.7549 0.7054 0.7088 0.5 -2.9 -2.8 2.7 0.0019 0.0018 0.0018 0.0017 0.0016 0,0016 0,0015 0.0015 0.0014 0.0014 -2.9 0.7257 0.7580 0.7389 0.7422 0.7704 0.7734 0.6 0.0026 0.0025 0.0024 0.0023 0.0023 0.0022 0.0021 0.0021 0.0020 0.0019 -2.8 0.7 0.7764 0.7794 0.8051 0.8078 0.7823 0.7852 0.0028 0.0027 0.0026 -2.7 0,7 0.8 0.0035 0.0034 0.0033 0.0032 0.0031 0.0030 0.0029 0.8 0.7881 0.7910 0.7939 0.7967 0.7995 0.8023 0.8106 0.8133 -2.6 0.0047 0.0045 0.0044 0.0043 0.0011 0.0040 0.0039 0.0038 0.0037 0.0036 -2.6 0.9 0.8159 0.8186 0.8212 0.8238 0.8264 0.8289 0.8315 0.8340 0.8365 0.8389 0.9 -2.5 0.0062 0.0060 0.0059 0.0057 0.0055 0,0054 0,0052 0.0051 0.0049 0.0048 -2.5 1.0 0,8413 0.8438 0,8461 0.8485 0.8508 0.8531 0.8554 0.8577 0.8599 0.8621 0,8810 0,8830 1.0 2.4 0.0082 0.0080 0.0078 0.0075 0.0073 0.0071 0.0069 0.0068 0.0066 0.0064 2.4 0.8686 0.8708 0.8770 0.8962 0.8980 1.1 0,8643 0.8665 0.8729 0.8749 0.8790 -2.3 0.0107 -2.2 0.0139 0.0102 0.0136 0.0132 1.1 1.2 0.0104 66000 0.0096 0.0094 0.0091 0.0089 0.0087 0.0084 -2.3 1.2 0,8849 0.8869 0.8888 0,8907 0.8925 0.8944 0.8097 0.9015 0.0129 0.0125 0.0122 0.0119 0.0116 -2.2 0.0150 0.0146 0.0143 -2.1 2.0 0.0113 0.0110 1.3 0.9032 0.9019 0.9066 0.9082 0.9099 0.9115 0.9131 0.9147 0.9162 0.9177 1.3 -2.1 2.0 0.0174 0.0170 0.0222 0.0217 0.0162 0.0207 0,0179 0.0166 0.0158 0.0154 1.4 0.9192 0.9207 0.9222 0.9236 0.9251 0.9265 0.9279 0.9292 0.9306 0.9319 1.4 0.0228 0.0212 0.0202 0.0197 0.0192 0.0188 0.0183 1.5 0.9332 0.9452 0.9554 0.9345 0.9357 0,9370 0.9382 0.9394 0.9406 0.9418 0.9429 0.9441 0.9535 0.9545 0.9633 1.5 0.0281 0.0274 0.0351 0.0344 0.0256 0.020O 0.0233 -1.9 -1.9 -1.8 0.0287 0.0268 0.0336 0.0262 0.0244 0.0239 0.0301 1.6 0.9463 0.9564 0.9474 0.9484 0.9582 0.9573 0.9495 0 9589 0 9s01 0.9525 0.9616 0.9505 0.9515 1.6 0.0350 0.0329 0.0322 0.0314 0,030 0.0307 0.0204 -1.8 1.7 0.9591 0.9599 0.9608 0,9625 1.7 -1.7 -1.6 -1.5 0.0367 -1.7 0.0475 0.0465 0.0455 -1.6 0.0582 0.0571 0.0559 -1.5 0.0446 0.0436 0.0427 0.0418 0.0400 0.0401 0.0392 0.0384 0.0375 1.8 0.9641 0.9649 0.9719 0.9726 0.9732 0.9656 0,9004 0.9671 0.9678 0.9686 0.9693 0.9099 0.9706 1.8 0.0548 0.006S 0.0537 0.0526 0.0655 0.0643 0.0630 0.0516 0.0505 0.0495 0.0485 1.9 0.9713 0.9738 0.9744 0.9750 0.9756 0.9761 0.9767 1.9 0.0618 0.0606 0.0594 2.0 0.9772 0.9778 0.9783 0,9788 0.9793 0.9798 0,9803 0.9808 0,9812 0.9817 2.0 -1.4 -1.3 -1.2 0.1151 0.0808 0.0793 0.0778 0.0764 0.0749 0.0735 0.0721 0.0708 0.0694 0.0681 -1.4 0.0823 -1.3 2.1 0.9821 0.9826 0.9864 0.9868 0.9871 0.9830 0.9834 0.9838 0.9842 0,9846 0.9881 0.9850 0,9854 0.9857 2.1 0.0001 0.0885 0.0869 0.1075 0.1056 0.1038 0.1230 0.1446 0.0968 0.0961 0.0934 0.0918 0.0853 0.0838 2.2 0,9861 0.9875 0.9878 0.9884 0.9887 0.9890 2.2 0.1131 0.1112 0.1314 0.1093 0.1292 0.1020 0.1210 0.1190 0.1003 0,0085 -1.2 2.3 0,9893 0,9806 0.9898 0.9901 0.9904 0.9906 0.9909 0.9911 0.9913 0.9916 2.3 -1.1 0.1357 0.1335 0.1271 0.1251 0.1170 -1.1 2.4 0.9918 0.9920 0.9922 0.9025 0.9927 0.9029 0.9031 0.9932 0.9934 0.9936 2.4 -1.0 0.1587 0.1562 0.1539 0.1515 0.1492 0.1469 0.1423 0.1401 0.1379 -1.0 0.9951 0.9952 0.9963 0.9964 0.9973 0.9974 0.9979 0.9980 0.9981 0.9086 0.9986 2.5 0.9938 0.9910 0.9941 0.9943 0.9945 0.9946 0.9948 0.9949 2.5 0.9 0.1736 0.1711 0.1685 0.2005 0.2296 0.2266 0.2236 0.2611 0.2946 0.2912 0.2877 0.1660 0.1635 0.1922 0.2206 0.1841 0.1814 0.1788 0.1762 0.1611 0.9 2.6 0.9953 0,9955 0.9956 0.9057 0.9950 0,9060 0.9961 0.9962 2.6 0.2119 0.2420 0.2033 0.2327 0.2643 0.8 0.2000 0.2061 0.1977 0.1949 0.1894 0.1867 0.8 0.9960 0.9970 0.9977 0.9978 0.9984 0.99s4 2.7 0,9065 0.9006 0.9967 0.9968 0.9971 0.9972 2.7 2.8 0.7 -0.6 0.2743 -0.5 -0.4 0.3 0.2 0.2389 0.2709 0.2358 0.2676 0.2177 0.2514 0.2483 0.2148 0.2451 -0.7 2.8 2.9 0.9974 0.9981 0.9975 0.9976 0.9977 0.9082 0.9979 0.9985 0.2578 0.2546 -0.6 0.9982 0.9083 0.9985 2.9 0.3085 0.3050 0.3015 0.2981 0.2843 0.2810 0.2776 -0.5 3.0 0.9989 0.9087 0,9990 0.9987 0.9987 0.9988 0.9988 0.9989 0.9989 0.9990 0.9990 3.0 0.3446 0.3409 0.3372 0.3336 0.3300 0.3264 0.3228 0.3192 0.3156 0.3121 -0.4 3.1 0,9901 0.9991 0.9992 0.9991 0.9994 0.9092 0.9992 0.9992 0.9093 0.9903 3.1 0.3821 0.4207 0.4168 0.3520 0.3483 0.3897 0.3869 -0.2 0.3783 0.3745 0.3707 0.3632 0.3594 0.4090 0.40G2 0.4013 0.3974 0.3669 0.3557 -0.3 3.2 0.9993 0.9903 0.9994 0.9991 0.9994 0.9995 0 0006 0.9904 0.9996 0.9995 3.2 0.4129 0.3936 00005 0 0005 00005 00006 00006 0 0006 00006 0 00006 0 0007 33 000
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