Q3&4 please

For each of the following questions: clearly indicate the probability distribution being used to solve the problem solve by hand, and verify your answer using MATLAB. 1. Two teams, A and B, play a series of games. If team B has a probability 0.4 of winning each game, is it to their advantage to play the best three out of five games or the best four out of seven, and why? Assume the outcomes of successive games are independent. 2. A quality control engineer works at a factory that bottles engine oil. The amount of oil is normally distributed with mean 40 litres and standard deviation of 0.05 litres. If the amount is less than 39.9 litres or more than 40.1 litres it is deemed to fail the quality control process. (a) Find the probability that a bottle will fail quality control (b) If the factory want to improve so that a bottle will fail 2% of the time, what must the quality control amounts be extended to? 3. Phone calls at your office occur at a rate of two calls per hour. If you leave the office for 30 minutes what is the probability you will miss a phone call? 4. If X is a uniform random variable with expected value (mean) 10 and variance 3. Find the probability P(X 8). Standard Normal Cumulative Probability Table Cumulative probabilities for NEGATIVE z-values are shown in the following table: 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 3.4 3.3 0.0003 0.0003 0.0003 0.0003 0.0003 0.0003 0.0003 0.0003 0.0003 0.0002 0.0005 0.0005 0.0005 0.0004 0.0004 0.0004 00004 0.0004 0.0004 0.0003 3.2 0.0007 0.0007 0.0006 0.0006 0.0006 0.0006 0.0006 0.0005 0.0005 0.0005 0.0010 0.0009 0.0009 0.0009 0.0008 0.0008 0.0008 0.0008 0.0007 0.0007 0.0013 0.0013 0.0013 0.0012 0.0012 0.0011 0.0011 0.0011 0.0010 0.0010 3.1 3.0 2.9 2.8 2.7 2.6 0.0019 0.0018 0.0018 0.00170.0016 0.0016 0.0015 0.0015 0.0014 0.0014 0.0026 0.0025 0.0024 0.0023 0.0023 0.0022 0.0021 0.0021 0.0020 0.0019 7 0.0035 0.0034 0.0033 0.0032 0.0031 00030 0.0029 0.0028 0.0027 0.0026 0.0047 0.0045 0.0044 0.0043 0.0041 0.0040 0.0039 0.0038 0.0037 0.0036 2.5 0.0062 0.0060 0.0059 0.0057 0.0055 0.0054 0.0052 0.0051 0.0049 0.0048 2.4 0.0082 0.0080 0.0078 0.0075 0.0073 0.0071 0.0069 0.0068 0.0066 0.0064 0.0107 0.0104 0.0102 0.0099 0.0096 0.0094 0.0091 0.0089 0.0087 0.0084 0.0139 0.0136 0.0132 0.0129 0.0125 0.0122 00119 00116 0.0113 0.0110 0.0179 0.0174 0.0170 0.0166 0.0162 0.0158 0.0154 0.0150 0.0146 0.0143 0 0.0228 0.0222 0.0217 0.0212 0.0207 0.0202 0.0197 0.0192 0.0188 0.0183 2.3 2.2 2.1 2. 1.9 1.8 1.7 0.0287 0.0281 0.0274 0.0268 0.0262 0.0256 0.0250 0.0244 0.0239 0.0233 0.0359 0.0351 0.0344 0.0336 0.0329 0.0322 0.0314 0.0307 0.0301 0.0294 0.0446 0.0436 0.0427 0.0418 0.0409 0.0401 0.0392 0.0384 0.0375 0.0367 1.6 0.0548 0.0537 0.0526 0.0516 0.0505 0.0495 0.0485 0.0475 0.0465 0.0455 0.0668 0.0655 0.0643 00630 0.0618 0.0606 0.0594 0.0582 0.0571 0.0559 1.5 0.0808 0.0793 0.0778 0.0764 0.0749 0.0735 0.0721 0.0708 0.0694 0.0681 1.3 0.0968 0.0951 0.09340.0918 0.0901 0.0885 00869 0.0853 0.0838 0.0823 0.1151 0.1131 0.1112 0.1093 0.1075 0.1056 0.1038 0.1020 0.1003 0.0985 0.1357 0.1335 0.1314 0.1292 0.1271 0.1251 0.1230 0.1210 0.1190 0.1170 1.0 0.1587 0.1562 0.1539 0.1515 0.1492 0.1469 01446 0.14230.140 0.1379 1.4 1.2 1.1 0.9 01841 0.1814 0.1788 0.1762 0.1736 0.1711 0.1685 0.1660 0.1635 0.1611 0.2119 0.2090 02061 0.2033 02005 0.1977 0.1949 0.1922 0.1894 0.1867 0.2420 0.2389 0.2358 0.2327 0.2296 02266 0.2236 02206 0.2177 0.2148 0.2743 0.2709 02676 0.2643 02611 02578 0.2546 02514 0.2483 0.2451 5 0.3085 0.3050 0.3015 0.2981 02946 02912 0.2877 0.2843 0.2810 0.2776 0.8 0.7 0.6 0. 0. 0.2 0.1 0.0 0.3446 0.3409 0.3372 0.3336 03300 0.3264 0.3228 03192 0.3156 0.3121 3 0.3821 0.3783 0.3745 0.3707 03669 0.3632 0.3594 0.3557 0.3520 0.3483 0.4207 0.4168 04129 0.4090 04052 04013 0.3974 0.3936 0.3897 0.3859 0.4602 0.4562 04522 0.4483 0.4443 04404 0.4364 0.4325 04286 0.4247 0.5000 0.4960 0.4920 0.4880 04840 04801 0.4761 04721 0.4681 0.4641 Standard Normal Cumulative Probability Table Cumulative probabilities for POSITIVE z-values are shown in the following table 0.00 0.5000 0.5040 0.5080 0.5120 0.5160 0.5199 0.5239 0.5279 0.5319 0.5359 0.5398 0.5438 0.5478 0.5517 0.5557 0.5596 0.5636 0.5675 0.5714 0.5753 0.5793 0.5832 05871 0.5910 0.5948 0.5987 0.6026 0.6064 0.6103 0.6141 0.6179 0.6217 0.6255 0.6293 0.6331 0.6368 0.6406 0.6443 0.6480 0.6517 0.6554 0.6591 0.6628 0.6664 0.6700 0.6736 0.6772 0.6808 0.6844 0.6879 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.0 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 0.6915 0.6950 0.6985 0.7019 0.7054 0.7088 0.7123 0.7157 0.7190 0.7224 0.7257 0.7291 0.7324 0.7357 0.7389 0.7422 0.7454 0.7486 0.7517 0.7549 0.7580 0.7611 0.7642 0.7673 0.7704 0.7734 0.7764 0.7794 0.7823 0.7852 0.7881 0.7910 0.7939 0.7967 0.7995 0.8023 0.8051 0.8078 0.8106 0.8133 0.8159 0.8186 0.8212 0.8238 0.8264 0.8289 0.8315 0.8340 0.8365 0.8389 1.0 1.1 1.2 1.3 1.4 0.8413 0.8438 0.8461 0.8485 0.8508 0.8531 0.8554 0.85770.8599 0.8621 0.8643 0.8665 0.8686 0.8708 0.8729 0.8749 0.8770 0.8790 0.8810 0.8830 0.8849 0.8869 0.8888 0.8907 0.8925 0.8944 0.8962 0.8980 0.8997 0.9015 0.9032 0.9049 0.9066 0.9082 0.9099 0.9115 0.9131 0.9147 0.9162 0.9177 0.9192 0.9207 0.9222 0.9236 0.9251 0.9265 0.9279 0.9292 0.9306 0.9319 1.5 0.9332 0.9345 0.9357 0.9370 0.9382 0.9394 0.9406 0.9418 09429 0.9441 0.9452 0.9463 0.9474 0.9484 0.9495 0.9505 0.9515 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 0.9641 0.9649 0.9656 0.9664 0.9671 0.9678 0.9686 0.9693 0.9699 0.9706 0.9713 0.9719 0.9726 0.9732 0.9738 0.9744 0.9750 0.9756 0.9761 0.9767 1.8 2.0 2.1 2.2 2.3 2.4 0.9772 0.9778 0.9783 0.9788 0.9793 0.9798 0.9803 0.9808 0.9812 0.9817 0.9821 0.9826 0.9830 0.9834 0.9838 0.9842 0.9846 0.9850 0.9854 0.9857 0.9861 0.9864 0.9868 0.9871 0.9875 0.9878 0.9881 0.9884 0.9887 0.9890 0.9893 0.9896 0.9898 0.9901 0.9904 0.9906 0.9909 0.9911 0.9913 0.9916 0.9918 0.9920 0.9922 0.9925 0.9927 0.9929 0.9931 0.9932 0.9934 0.9936 2.5 2.6 2.7 2.8 2.9 0.9938 0.9940 0.9941 0.9943 0.9945 0.9946 0.9948 0.9949 0.9951 0.9952 0.9953 0.9955 0.9956 0.99570.9959 0.9960 0.9961 0.9962 0.9963 0.9964 0.9965 0.9966 0.9967 0.9968 0.9969 0.9970 0.9971 0.9972 0.9973 0.9974 0.9974 0.9975 0.9976 0.9977 0.9977 0.9978 0.9979 0.9979 0.9980 0.9981 0.998 0.9982 0.9982 0.9983 0.9984 0.9984 0.9985 0.9985 0.9986 0.9986 3.0 3.1 3.2 3.3 3.4 0.9987 0.9987 0.9987 0.9988 0.9988 0.9989 0.9989 0.9989 0.9990 0.9990 0.9990 0.9991 0.9991 0.9991 0.9992 0.9992 0.9992 0.9992 0.9993 0.9993 0.9993 0.9993 0.9994 0.9994 0.9994 0.9994 0.9994 0.9995 0.9995 0.9995 0.9995 0.9995 0.9995 0.9996 0.9996 0.9996 0.9996 0.9996 0.9996 0.9997 0.9997 0.9997 0.9997 0.9997 0.9997 0.9997 0.9997 0.9997 0.9997 0.9998