\fPart 4: Prototype evaluation A. You've recently changed the supplier of the generator that you use in the lifting equipment. You have gathered experimental data of energy savings for both generator prototypes (original supplier prototype A in Table 7, and new supplier prototype B in Table 8). a. Calculate the mean and standard deviation for both prototypes. b. For both prototypes, calculate the probability of generating energy savings of less than 50 Wh. C . For both prototypes, calculate the probability of generating energy savings of more than 100 Wh. d. Use hypothesis testing to establish whether the difference between the two prototypes' mean energy savings is significant or not (test for a significance value of ed n a = 0.05). You can assume that the data is normally distributed. naqmoo 26 belleb B. You notice that prototype B occasionally seizes up, thus failing quality control. Given a failure rate of P percent (see Table 9), calculate: a. the chance of picking exactly 0 faulty items from a selection of 30 prototypes. b. the chance of picking less than 3 faulty items from a selection of 30 prototypes. c. the chance of picking more than 5 faulty items from a selection of 30 prototypes C. The sales team has requested a detailed report of the findings in Part 4 A. and B. to hand out to potential customers. The report must be understandable by non-technical readers; therefore, it should contain: explanations of the different terms used (i.e., mean, standard deviation, hypothesis testing, normally and binomially distributed variables) . a description of the methods used (i.e., how to use the relevant mathematical formulas and/or Excel functions) interpretations of the results (i.e., using whole sentences to describe the numerical results). .8 oldsT ni bobivong ei g 113 ning erl el forW .s END OF ASSIGNMENT uper erdt al terivy (Tables on following pages)Table 8: Energy savings (Wh) of prototype B Loveli Row 21-35 36-50 51-65 Wh) 66-80 B1-95 (Wh) 96-110 111-125 126-140 (Wh) (Wh) (Wh) (Wh) (Wh) (Wh) DS NZ 1 0 0 9 21 17 8 0 1 6 26 18 3 0 0 6 17 21 6 0 0 UI A W N 0 3 8 21 13 1 0 0 2 14 22 6 1 0 6 0 1 8 23 16 6 2 0 7 0 2 8 23 14 7 0 0 8 0 4 6 23 15 6 2 1 1 1 6 25 19 5 2 1 10 1 0 6 18 17 7 0 0 0 2 2 1 4 19 18 6 1 0 13 0 0 o O 00 00 14 3 0 0 V V 15 0 22 w 0 0 16 1 2 6 21 4 1 8 00 UT 17 1 4 23 V 1 18 0 4 6 18 16 7 2 0 19 0 3 23 17 5 0 20 0 1 7 25 18 6 2 0 Table 9: Failure rate P Row P (%) 1 13 2 11 A 3 9 4 15 UI 11 6 6 7 10 8 6 9 16 10 8 11 10 12 6 13 14 14 9 15 10 16 8 17 5 18 8 19 12 20 6 Page 11 of 11Standard Normal Cumulative Probability Table Cumulative probabilities for NEGATIVE z-values are shown in the following table: 0.01 0.02 10.03 10.04 0.05 0.06 0.07 0.08 0.09 0.00 D.OOD3 0.0003 0.0003 0.0003 0.0003 0.0003 0.DO03 0.0003 0.0002 3.4 -3. D.0005 0.0005 0.0005 0.0904 0.0004 0.0904 0.0004 0.D004 0.0004 0.DO03 -3.2 D.OOD7 0.0007 0.0006 0.0006 0.0006 D.DO06 0.0905 0.0005 0.D005 -3.1 D.0010 0.0008 0.0009 0.0009 0.0008 0.DOOS 0.0003 0.DO07 0 0007 0.0013 0.0013 0.0013 0.0012 0.0012 0.001 1 0.DO1 1 0.001 0.DO 10 0.DQ 10 -2.9 D.0019 0.0018 0.0013 0.0017 0.0016 0. DO 16 0.0015 0.0015 0.DO 14 0.0014 -2.8 D.0026 0.0025 0.0024 0.0023 0.0023 0.0022 0.0021 0.6021 0.DO20 0.DQ 19 -2.7 D.0035 0.0034 0.0033 0.0032 0.0031 0.0030 0.0029 0.DO28 0.DO27 0.0026 2.6 D.0047 0.0045 0.0044 0.0043 0.0041 0.0040 0.0039 0.0038 0.DO37 0.0036 -2.5 D.0062 0.0060 0.0050 0.0057 0.0065 0.0054 0.0052 0.6051 0.0049 0.0048 2.4 D.0032 0.0080 0.0078 0.0075 0.0073 D.DOT 0.D068 0.0063 D.0066 0.D064 2.3 D.0107 0.0104 0.0102 0.0099 0.0026 0.0094 0.Doe 0.D089 0.0087 0.D034 -2.2 D.0139 0.0136 0.0132 0.0129 0.0125 0.D122 0.0119 0.01 16 0.01 13 0.D1 10 -2.1 D.0179 0.0174 0.0170 0.0166 D.0162 0.0158 0.0154 0.0150 0.D146 0.D143 -2.0 D.0228 0.0222 0.0217 0.0212 0.0207 0.0202 0.0197 0.0192 0.0198 0.0183 -1.9 D.0287 0.0281 0.0274 0.0268 0.0262 0.0256 0.0250 0.0244 0.0239 0.0233 -1.8 D.0359 0.0351 0.0344 0.0336 0.0329 0.0322 0.0814 0.D807 0.0301 0.0294 -1.7 0.0446 0.0435 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 0.0506 10.0496 0.0485 0.0475 0.D465 0.D455 1.5 D.0668 0.0655 0.0643 0.0630 0.0618 0.0608 0.0584 0.0582 0.057 1 0.D559 -1.4 0.0303 0.0793 0.0773 0.0764 0.0749 0.0735 0.0721 0.0708 0.0694 0.0681 1.3 0.0968 D.0951 0.0934 0.0918 0.0901 0.0885 0.0869 0.0853 0.0538 0.0823 1.2 D. 1 151 0.1 131 D. 1112 0.1093 0.1075 0. 1056 0.1038 0.1020 0.1003 1.1 0.1357 0.1335 0.1314 0.1292 10.1271 0.0985 0.1251 0.1230 0.1210 0.1190 1.0 0. 1587 0.1562 0.1539 0.1515 0.1492 0. 1469 0. 1446 0.1170 0.1423 0 1401 0.1379 0.9 D. 1841 0. 1814 0.1788 0.1762 0.1736 10.1711 0. 1685 0.1560 D.2119 0.2090 0.2061 0.2038 0.1635 0.2005 0.1977 0.1948 0.1611 0.8 0.1922 D.2420 0.2327 0.1894 0.2389 0.2296 0.2286 0.2236 0.1867 -0.7 6.2368 0.2206 0.217 7 0.6 D.2743 0.2709 0.2676 0.2643 0.2611 0.2578 10 2148 0. 2546 0 2514 0.3035 0.3050 0.3015 0.2981 0.2946 0.2433 0.2912 0.2451 10.287 7 0.2843 0. 28 10 0.2776 0.3446 0.3409 0.3372 0.2326 0.3300 0.3264 0.3229 0.3192 0.3 0.3745 10.3156 D.3821 0.3783 0.3707 0.3669 0.3632 0 3121 0.3594 0.3557 02 D.4207 0.4168 0.4129 0.4020 0.4052 0.3520 0.4013 0.3483 0.3974 0.1 D.4602 0.4562 0.4522 0 3836 0.4483 0.4443 0.3897 0.4404 0.4364 0.3959 0.4325 D.4960 0.4920 0.4280 0. 4286 0.0 D.50D0 0.4840 0.4801 0.4247 0.4761 0.4721 0 4631 0.4641Standard Normal Cumulative Probability Table Cumulative probabilities for POSITIVE z-values are shown in the following table: Z 0.00 D.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.0 D.50DO D.5040 0.5080 0.5120 0.5160 0.5199 0.5239 0.5279 0.5319 0.6359 0.1 D.5398 0.5438 0.5478 0.5517 0.5567 0.6596 0.5636 0.5675 0.5714 0.5753 0.2 D.5793 0.5832 D.5871 0.5910 0.5948 0.5987 0.6026 0.6064 0.6103 0.6141 0.3 D.6179 0.6217 0.6255 0.6293 0.6331 0.6368 0.8408 0.6443 0.6480 0.6517 0.4 D.6554 0.6591 0.6628 0.6664 0.6700 0.6736 0.6772 0.6808 0.6844 0.6879 0.5 D.6915 0.6950 0.6935 0.7019 0.7054 0.7038 0.7123 0.7157 0.7190 0.7224 0.6 D.7257 0.7291 0.7324 0.7367 0.7389 0.7422 0.7454 0.7486 0.7517 0.7549 0.7 D.7580 0.7611 0.7642 0.7673 0.7704 0.7734 0.7764 0.7794 0.7823 0.7852 0.8 D.7831 0.7910 0.7939 0.7967 0.7995 0.8023 0.8051 0.8078 0.8106 0.8123 0 9 D.8169 0.5186 0.3212 0.3238 0.8264 0.8289 . 08315 0.8340 0.8365 0.8389 D.8413 0.8438 0.8461 0.3485 0.8503 0.8531 1 0.8554 0.8577 0.8599 0.2621 1.1 0.3643 0.8665 0.8686 0.3708 0.8729 0.8749 0.8770 0.8790 0.8510 0.8930 1.2 0.8549 0.3869 0.3888 0.8907 0.5926 0.2944 0.8962 0.2980 0.3897 0 9015 1.3 D.9032 0.9049 0.9066 0.9082 0.9099 0.9115 0.9131 0.9147 0.9162 0.9177 1.4 D.9192 0.9207 0.9222 0.9236 0.9251 0.9265 0 9279 0 9292 0.9306 0.9319 1-5 D.0332 0.9345 0.9367 0.9370 0.9382 0.9394 0 9406 0.9418 0.9429 0.9441 1.6 0.9452 0.9463 0.9474-- 0.9484 0.9495 0 9505 0.9515 0.9525 0.9535 0.9545 1.7 D.9554 0.9564 0.9573 0.9532 0.9591 0.9590 0 9608 0 96 16 0.9625 18 0.9633 D.9641 0.9649 0.9656 0.9664 0.9671 0.9678 0.9686 0.9693 0.9609 1.9 0.9706 0.9713 0.9719 0.9726 0.9732 0.9738 0.9744 0.9750 0.9756 0.2761 0.9767 2.0 D.9772 0.9778 0.9783 0.9783 0.9793 D.9798 0.9303 0.9808 0.98 12 251 D.9821 0.9826 0.9830 10.9834 0.9817 0.9836 0.9842 0.9846 0.9850 0.9354 D.9861 0.9364 0.9868 1 0.9871 0.9857 2.2 0.9875 D.9873 0.9881 0.9884 0.9387 2.3 0.9803 0.9396 0.9398 0.9901 0.9904 0.9890 0.0906 0.8909 0.9811 0.9813 2.4 D.9918 0.0920 0.9922 0.9925 0.9927 D.0929 10.9931 0.9916 0.9932 0.9934 0.9836 2.5 D.9938 0.9940 0.9941 0.9943 0.9945 D.2946 0.9848 0.8949 0.9851 2.6 D.9963 0.9955 0.9956 0.8957 0.8959 D.9860 0.0961 0.8952 0 0962 2.7 D. 9965 0.9960 0.9967 0.9963 10.9969 0.9863 0.9970 0.8971 0.9964 0.9872 2.8 0.9975 0.8976 0,8977 10.9877 0.9873 D.9974 10.8978 0.9879 0 9874 0.8979 2.9 D.9981 0.9982 0.9932 0.9983 0.9930 0.9984 0.9984 0.9936 0.9981 0.9835 0.9836 0.2936 3.0 D.9987 0.9987 0.8987 0.9983 0.9939 0. 2985 0.9920 0.9891 0.9891 0.9901 0.9892 0.8982 0.9892 0.8980 0.9990 3.2 0.0983 0.9984 0.9892 0.0993 0.9994 0.9994 0.8994 0.8093 0.9094 0.9895 0.8993 3.3 D.8925 0.9925 0.9895 0.9896 0.9986 0.9096 0.2895 0.9096 0.9896 0.9895 3.4 D.9997 0.gee7 0.9987 0.9097 0.8987 0.9097 0.0996 0.9897 0.9897 0.9097 0.9897 9 O EPIC