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Steel rods are manufactured with a mean length of 22 centimeter (cm). Because of variability in the manufacturing process, the lengths of the rods are approximately normally distributed with a standard deviation of 0.06 cm. Click the icon to view a table of areas under the normal curve. (a) What proportion of rods has a length less than 21.9 cm? (Round to four decimal places as needed.)

Steel rods are manufactured with a mean length of 22 centimeter (cm). Because of variability in the manufacturing process, the lengths of the rods are approximately normally distributed with a standard deviation of 0.06 cm. Click the icon to view a table of areas under the normal curve. (a) What proportion of rods has a length less than 21.9 cm? (Round to four decimal places as needed.)

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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10/9/23, 11:06 AM TABLE V -2.6 -2.3 .02 .07 .08 .09 0.0019 -34 0.0003 0.0003 0.0003 0.0003 0.0003 0.0003 0.0003 0.0003 0.0003 0.0002 -33 0.0005 0.0005 0.0005 0.0004 0.0004 0.0004 0.0004 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 -3.1 0.0010 0.0009 0.0009 0.0009 0.0008 0.0008 0.0008 0.0008 0.0007 0.0007 -3.0 0.0013 0,0013 0.0013 0.0012 0.0012 0.0011 0.0011 0.0011 0.0010 0.0010 -2.9 0.0019 0.0018 0,0018 0.0017 0.0016 0.0016 0.0015 0.0015 0.0014 0.0014 -2.8 0.0026 0.0025 0.0024 0.0023 0.0023 0.0022 0.0021 0.0021 0.0020 0.0035 0.0034 0.0033 0.0032 0.0031 0.0030 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 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 -2.3 0.0107 0.0104 0.0102 0.0099 0.0096 0.0094 0.0091 0.0089 0.0087 0.0084 -2.2 0.0139 0.0136 0.0132 0.0129 0.0125 00122 0.0119 0.0116 0.0113 0.0110 -2.1 0.0179 0.0174 0.0170 0.0166 0.0162 0.0158 0.0154 0.0150 0.0146 0.0143 -2.0 0.0228 0.0222 0,0217 0,0212 0.0207 0.0202 0.0197 0.0192 0.0188 0.0183 -1.9 0.0287 0,0281 0.0274 0.0268 0,0262 0.0256 0.0250 0.0244 0.0239 0.0233 -1.8 0.0359 0.0351 0.0344 0.0336 0.0329 0.0322 0.0314 0.0307 0.0301 0.0294 -1.7 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 -1.5 0.0668 0.0655 0.0643 0.0630 0.0618 0.0485 0.0475 0.0465 0.0455 0.0594 0.0582 0.0571 0.0559 0.1 0.2 0.3 .00 Standard Normal Distribution 03 .04 .05 -1.4 0.0808 0.0793 0.0778 0.0764 0.0749 0.0735 -1.3 0.0968 0.0951 0.0934 0,0918 0,0901 0.0885 -1.2 0.1151 0.1131 0.1112 0.1093 0.1075 -1.1 0.1357 0.1335 0.1314 0.1292 0.1271 -1.0 0.1587 0.1562 0.1539 0.1515 0,1492 -0.9 0.1841 0.1814 0.1788 0.1762 0.1736 0.1711 0.1685 0.1660 0.1635 0.1611 -0.8 0.2119 0.2090 0.2061 0.2033 0.2005 0.1977 0.1949 0.1922 0.1894 0.1867 -0.7 0.2420 0.2389 0.2358 0.2327 0.2296 0.2266 0.2236 0.2206 0.2177 02148 -0.6 0.2743 0.2709 0.2676 0.2643 0.2611 0.2578 0.2546 0.2514 02483 0.2451 -0.5 0.3085 0.3050 0.3015 0.2981 0.2946 0.2912 0.2877 0.2843 0.2810 0.2776 -0.4 0.3446 0.3409 0.3372 0.3336 0 3300 0.3264 0.3228 0.3192 0.3156 03121 -0.3 0.3783 0.3745 0.3707 0.3669 0.3632 0.3594 0.3557 0.3520 0.3483 <-0.2 0.4207 0.4168 0.4129 0.4090 04052 0.3974 0.3936 0.3897 0.3859 -0.1 0.4602 0.4562 0.4522 0.4483 0.4443 0.4404 0.4364 0.4325 0.4286 0.4247 0.5000 0,4920 0,4880 0.4840 04761 04721 0.4681 0.4641 0.5000 05040 0.5080 0.5120 0.5160 0.5199 05239 0.5279 05319 0.5359 0.5398 0.5438 0.5478 0.5517 0.5557 0.5590 0.5636 0.5675 0.571 0.5753 0.5832 0.5871 0.5910 0.5948 0.5987 0.6026 0.6064 0.6103 0.6141 06179 0.6217 06255 0.6293 06331 0.6368 0.6406 0.6443 0.6480 0.6517 0.4 0.6554 0,6591 0.6628 0.6664 0.6700 0.6736 0.6772 0.6808 0.6844 0.6879 0.6985 0,7019 0.7054 0.7123 0.7157 0.7190 0.7224 0.7324 0.7357 0.7389 0.7422 0.7454 0.7486 0.7517 0.7549 0.7 0.7580 0.7611 0.7642 0.7673 0.7704 0.7734 0.7764 0.7794 0.7823 0.7852 0.8 0.7881 0.7910 0.7939 0.7967 0.7995 0.8023 0.8051 0.8078 0.8106 0.8133 0.9 0.8159 0.8186 0.8212 0.8238 0.8264 0.8289 0.8315 0.8340 0.8365 0.8389 1.0 0.8413 0.8438 0.8461 0.8531 0.8554 0.8577 0.8599 0.8621 1.1 0.8643 0.8665 0.8686 0.8708 0.8729 0.8749 0.8770 0.8790 08810 0.8830 1.2 0.8849 0.8869 0.8888 0,8907 0.8925 0.8944 0.8962 0.8980 08997 0.9015 1.3 0.9032 0.9049 0.9066 0.9082 0.9099 0.9115 0.9131 0.9147 0.9162 0.9177 1.4 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 09418 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 0.9554 0.9564 0.9573 0.9582 0.9591 0.9599 0.9608 0.9616 0.9625 0.9633 1.8 0,9641 0.9649 0.9656 0.9664 0.9671 0.9678 0.9686 0.9693 0.9699 0.9706 1.9 0.9713 0.9719 0.9726 0.9732 0.9738 0.9744 0.9750 0.9756 0.9761 0.9767 0.5 0.6915 0,6950 0.6 0.7257 0.8508 31 3.2 .00 90⁰ Tables of Areas under the Normal Curve 0.9890 2.0 0.9772 0.9778 0.9783 0.9788 0.9793 0.9798 0.9803 0.9808 0.9812 2.1 0.9821 0.9826 0.9830 0.9834 0.9838 0.9842 0.9846 0.9850 0.9854 22 0.9861 0.9864 0.9868 0.9871 0.9875 0.9878 0.9881 0.9884 0.9887 2.3 0.9893 0.9896 0.9898 0.9901 0.9904 0.9900 0.9909 0.9911 0.9913 0.9916 2.4 0.9918 0.9920 0.9922 0.9925 0.9927 0.9929 0.9931 0.9932 0.9934 0.9936 2.5 0.9938 0.9940 0.9941 0.9943 0.9945 0.9946 0.9948 0.9949 0.9951 0.9952 26 0.9953 0.9955 0.9956 0.9957 0.9959 0.9960 0.9961 0.9962 0.9963 0.9964 27 0.9965 0.9966 0.9967 0.9968 0.9969 0.9970 0.9971 0.9972 0.9973 0.9974 2.8 0.9974 0.9975 0.9976 0.9977 0.9977 0.9978 0.9979 0.9979 09980 0.9981 2.9 0.9981 0.9982 0.9982 0.9983 0.9984 0.9984 0.9985 0.9985 09986 0.9986 L666'0 3.0 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 3.3 0.9995 0.9995 0.9995 0.9996 0.9996 0.9996 0.9996 0.9996 0.9996 0.9997 3.4 0.9997 0.9997 0.9997 0.9997 0.9997 0.9998 0.9997 0.9997 0.9997 .01 .02 .04 .06 07 .08 .09 03 0.0721 0.0708 0.0694 0.0681 0.0869 0.0853 0.0838 0.0823 0.1038 0.1020 0.1003 0.0985 0.1251 0.1230 0.1210 0.1190 0.1170 0.1469 0.1446 0.1423 0.1401 0.1379 .05 0.9817 0.9857
Transcribed Image Text:10/9/23, 11:06 AM TABLE V -2.6 -2.3 .02 .07 .08 .09 0.0019 -34 0.0003 0.0003 0.0003 0.0003 0.0003 0.0003 0.0003 0.0003 0.0003 0.0002 -33 0.0005 0.0005 0.0005 0.0004 0.0004 0.0004 0.0004 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 -3.1 0.0010 0.0009 0.0009 0.0009 0.0008 0.0008 0.0008 0.0008 0.0007 0.0007 -3.0 0.0013 0,0013 0.0013 0.0012 0.0012 0.0011 0.0011 0.0011 0.0010 0.0010 -2.9 0.0019 0.0018 0,0018 0.0017 0.0016 0.0016 0.0015 0.0015 0.0014 0.0014 -2.8 0.0026 0.0025 0.0024 0.0023 0.0023 0.0022 0.0021 0.0021 0.0020 0.0035 0.0034 0.0033 0.0032 0.0031 0.0030 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 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 -2.3 0.0107 0.0104 0.0102 0.0099 0.0096 0.0094 0.0091 0.0089 0.0087 0.0084 -2.2 0.0139 0.0136 0.0132 0.0129 0.0125 00122 0.0119 0.0116 0.0113 0.0110 -2.1 0.0179 0.0174 0.0170 0.0166 0.0162 0.0158 0.0154 0.0150 0.0146 0.0143 -2.0 0.0228 0.0222 0,0217 0,0212 0.0207 0.0202 0.0197 0.0192 0.0188 0.0183 -1.9 0.0287 0,0281 0.0274 0.0268 0,0262 0.0256 0.0250 0.0244 0.0239 0.0233 -1.8 0.0359 0.0351 0.0344 0.0336 0.0329 0.0322 0.0314 0.0307 0.0301 0.0294 -1.7 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 -1.5 0.0668 0.0655 0.0643 0.0630 0.0618 0.0485 0.0475 0.0465 0.0455 0.0594 0.0582 0.0571 0.0559 0.1 0.2 0.3 .00 Standard Normal Distribution 03 .04 .05 -1.4 0.0808 0.0793 0.0778 0.0764 0.0749 0.0735 -1.3 0.0968 0.0951 0.0934 0,0918 0,0901 0.0885 -1.2 0.1151 0.1131 0.1112 0.1093 0.1075 -1.1 0.1357 0.1335 0.1314 0.1292 0.1271 -1.0 0.1587 0.1562 0.1539 0.1515 0,1492 -0.9 0.1841 0.1814 0.1788 0.1762 0.1736 0.1711 0.1685 0.1660 0.1635 0.1611 -0.8 0.2119 0.2090 0.2061 0.2033 0.2005 0.1977 0.1949 0.1922 0.1894 0.1867 -0.7 0.2420 0.2389 0.2358 0.2327 0.2296 0.2266 0.2236 0.2206 0.2177 02148 -0.6 0.2743 0.2709 0.2676 0.2643 0.2611 0.2578 0.2546 0.2514 02483 0.2451 -0.5 0.3085 0.3050 0.3015 0.2981 0.2946 0.2912 0.2877 0.2843 0.2810 0.2776 -0.4 0.3446 0.3409 0.3372 0.3336 0 3300 0.3264 0.3228 0.3192 0.3156 03121 -0.3 0.3783 0.3745 0.3707 0.3669 0.3632 0.3594 0.3557 0.3520 0.3483 <-0.2 0.4207 0.4168 0.4129 0.4090 04052 0.3974 0.3936 0.3897 0.3859 -0.1 0.4602 0.4562 0.4522 0.4483 0.4443 0.4404 0.4364 0.4325 0.4286 0.4247 0.5000 0,4920 0,4880 0.4840 04761 04721 0.4681 0.4641 0.5000 05040 0.5080 0.5120 0.5160 0.5199 05239 0.5279 05319 0.5359 0.5398 0.5438 0.5478 0.5517 0.5557 0.5590 0.5636 0.5675 0.571 0.5753 0.5832 0.5871 0.5910 0.5948 0.5987 0.6026 0.6064 0.6103 0.6141 06179 0.6217 06255 0.6293 06331 0.6368 0.6406 0.6443 0.6480 0.6517 0.4 0.6554 0,6591 0.6628 0.6664 0.6700 0.6736 0.6772 0.6808 0.6844 0.6879 0.6985 0,7019 0.7054 0.7123 0.7157 0.7190 0.7224 0.7324 0.7357 0.7389 0.7422 0.7454 0.7486 0.7517 0.7549 0.7 0.7580 0.7611 0.7642 0.7673 0.7704 0.7734 0.7764 0.7794 0.7823 0.7852 0.8 0.7881 0.7910 0.7939 0.7967 0.7995 0.8023 0.8051 0.8078 0.8106 0.8133 0.9 0.8159 0.8186 0.8212 0.8238 0.8264 0.8289 0.8315 0.8340 0.8365 0.8389 1.0 0.8413 0.8438 0.8461 0.8531 0.8554 0.8577 0.8599 0.8621 1.1 0.8643 0.8665 0.8686 0.8708 0.8729 0.8749 0.8770 0.8790 08810 0.8830 1.2 0.8849 0.8869 0.8888 0,8907 0.8925 0.8944 0.8962 0.8980 08997 0.9015 1.3 0.9032 0.9049 0.9066 0.9082 0.9099 0.9115 0.9131 0.9147 0.9162 0.9177 1.4 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 09418 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 0.9554 0.9564 0.9573 0.9582 0.9591 0.9599 0.9608 0.9616 0.9625 0.9633 1.8 0,9641 0.9649 0.9656 0.9664 0.9671 0.9678 0.9686 0.9693 0.9699 0.9706 1.9 0.9713 0.9719 0.9726 0.9732 0.9738 0.9744 0.9750 0.9756 0.9761 0.9767 0.5 0.6915 0,6950 0.6 0.7257 0.8508 31 3.2 .00 90⁰ Tables of Areas under the Normal Curve 0.9890 2.0 0.9772 0.9778 0.9783 0.9788 0.9793 0.9798 0.9803 0.9808 0.9812 2.1 0.9821 0.9826 0.9830 0.9834 0.9838 0.9842 0.9846 0.9850 0.9854 22 0.9861 0.9864 0.9868 0.9871 0.9875 0.9878 0.9881 0.9884 0.9887 2.3 0.9893 0.9896 0.9898 0.9901 0.9904 0.9900 0.9909 0.9911 0.9913 0.9916 2.4 0.9918 0.9920 0.9922 0.9925 0.9927 0.9929 0.9931 0.9932 0.9934 0.9936 2.5 0.9938 0.9940 0.9941 0.9943 0.9945 0.9946 0.9948 0.9949 0.9951 0.9952 26 0.9953 0.9955 0.9956 0.9957 0.9959 0.9960 0.9961 0.9962 0.9963 0.9964 27 0.9965 0.9966 0.9967 0.9968 0.9969 0.9970 0.9971 0.9972 0.9973 0.9974 2.8 0.9974 0.9975 0.9976 0.9977 0.9977 0.9978 0.9979 0.9979 09980 0.9981 2.9 0.9981 0.9982 0.9982 0.9983 0.9984 0.9984 0.9985 0.9985 09986 0.9986 L666'0 3.0 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 3.3 0.9995 0.9995 0.9995 0.9996 0.9996 0.9996 0.9996 0.9996 0.9996 0.9997 3.4 0.9997 0.9997 0.9997 0.9997 0.9997 0.9998 0.9997 0.9997 0.9997 .01 .02 .04 .06 07 .08 .09 03 0.0721 0.0708 0.0694 0.0681 0.0869 0.0853 0.0838 0.0823 0.1038 0.1020 0.1003 0.0985 0.1251 0.1230 0.1210 0.1190 0.1170 0.1469 0.1446 0.1423 0.1401 0.1379 .05 0.9817 0.9857
Steel rods are manufactured with a mean length of 22 centimeter (cm). Because of variability in the manufacturing process, the lengths of the rods are approximately normally distributed with a standard deviation of 0.06 cm. Click the icon to view a table of areas under the normal curve. (a) What proportion of rods has a length less than 21.9 cm? (Round to four decimal places as needed.)
Transcribed Image Text:Steel rods are manufactured with a mean length of 22 centimeter (cm). Because of variability in the manufacturing process, the lengths of the rods are approximately normally distributed with a standard deviation of 0.06 cm. Click the icon to view a table of areas under the normal curve. (a) What proportion of rods has a length less than 21.9 cm? (Round to four decimal places as needed.)
Expert Solution
Step 1: Information given is

Mean(straight mu)=22

standard deviation(straight sigma)=0.06

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Follow-up Question
Steel rods are manufactured with a mean length of 22 centimeter (cm). Because of variability in the manufacturing process, the lengths of the rods are approximately normally distributed with a standard deviation of 0.06 cm. Click the icon to view a table of areas under the normal curve. (a) What proportion of rods has a length less than 21.9 cm? 0.0475 (Round to four decimal places as needed.) (b) Any rods that are shorter than 21.86 cm or longer than 22.14 cm are discarded. What proportion of rods will be discarded? 0.0196 (Round to four decimal places as needed.) (c) Using the results of part (b), if 5000 rods are manufactured in a day, how many should the plant manager expect to discard? 98 (Use the answer from part b to find this answer. Round to the nearest integer as needed.) (d) If an order comes in for 10,000 steel rods, how many rods should the plant manager expect to manufacture if the order states that all rods must be between 21.9 cm and 22.1 cm? (Round up to the nearest integer.)
Transcribed Image Text:Steel rods are manufactured with a mean length of 22 centimeter (cm). Because of variability in the manufacturing process, the lengths of the rods are approximately normally distributed with a standard deviation of 0.06 cm. Click the icon to view a table of areas under the normal curve. (a) What proportion of rods has a length less than 21.9 cm? 0.0475 (Round to four decimal places as needed.) (b) Any rods that are shorter than 21.86 cm or longer than 22.14 cm are discarded. What proportion of rods will be discarded? 0.0196 (Round to four decimal places as needed.) (c) Using the results of part (b), if 5000 rods are manufactured in a day, how many should the plant manager expect to discard? 98 (Use the answer from part b to find this answer. Round to the nearest integer as needed.) (d) If an order comes in for 10,000 steel rods, how many rods should the plant manager expect to manufacture if the order states that all rods must be between 21.9 cm and 22.1 cm? (Round up to the nearest integer.)
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Follow-up Question
Steel rods are manufactured with a mean length of 22 centimeters (cm). Because of variability in the manufacturing process, the lengths of the rods are approximately normally distributed with a standard deviation of 0.06 cm. ### Questions and Solutions: (a) **What proportion of rods has a length less than 21.9 cm?** - Answer: 0.0475 (rounded to four decimal places). (b) **Any rods that are shorter than 21.86 cm or longer than 22.14 cm are discarded. What proportion of rods will be discarded?** - Answer: 0.0196 (rounded to four decimal places). (c) **Using the results of part (b), if 5000 rods are manufactured in a day, how many should the plant manager expect to discard?** - Answer: 98 rods (use the answer from part b and round to the nearest integer). (d) **If an order comes in for 10,000 steel rods, how many rods should the plant manager expect to manufacture if the order states that all rods must be between 21.9 cm and 22.1 cm?** - Solution: [Round up to the nearest integer.] **Note:** There is an icon mentioned to view a table of areas under the normal curve, likely used to find the probabilities needed for these calculations.
Transcribed Image Text:Steel rods are manufactured with a mean length of 22 centimeters (cm). Because of variability in the manufacturing process, the lengths of the rods are approximately normally distributed with a standard deviation of 0.06 cm. ### Questions and Solutions: (a) **What proportion of rods has a length less than 21.9 cm?** - Answer: 0.0475 (rounded to four decimal places). (b) **Any rods that are shorter than 21.86 cm or longer than 22.14 cm are discarded. What proportion of rods will be discarded?** - Answer: 0.0196 (rounded to four decimal places). (c) **Using the results of part (b), if 5000 rods are manufactured in a day, how many should the plant manager expect to discard?** - Answer: 98 rods (use the answer from part b and round to the nearest integer). (d) **If an order comes in for 10,000 steel rods, how many rods should the plant manager expect to manufacture if the order states that all rods must be between 21.9 cm and 22.1 cm?** - Solution: [Round up to the nearest integer.] **Note:** There is an icon mentioned to view a table of areas under the normal curve, likely used to find the probabilities needed for these calculations.
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Follow-up Question
Steel rods are manufactured with a mean length of 22 centimeter (cm). Because of variability in the manufacturing process, the lengths of the rods are approximately normally distributed with a standard deviation of 0.06 cm. Click the icon to view a table of areas under the normal curve. (a) What proportion of rods has a length less than 21.9 cm? 0.0475 (Round to four decimal places as needed.) (b) Any rods that are shorter than 21.86 cm or longer than 22.14 cm are discarded. What proportion of rods will be discarded? 0.0196 (Round to four decimal places as needed.) (c) Using the results of part (b), if 5000 rods are manufactured in a day, how many should the plant manager expect to discard? (Use the answer from part b to find this answer. Round to the nearest integer as needed.)
Transcribed Image Text:Steel rods are manufactured with a mean length of 22 centimeter (cm). Because of variability in the manufacturing process, the lengths of the rods are approximately normally distributed with a standard deviation of 0.06 cm. Click the icon to view a table of areas under the normal curve. (a) What proportion of rods has a length less than 21.9 cm? 0.0475 (Round to four decimal places as needed.) (b) Any rods that are shorter than 21.86 cm or longer than 22.14 cm are discarded. What proportion of rods will be discarded? 0.0196 (Round to four decimal places as needed.) (c) Using the results of part (b), if 5000 rods are manufactured in a day, how many should the plant manager expect to discard? (Use the answer from part b to find this answer. Round to the nearest integer as needed.)
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Follow-up Question
Steel rods are manufactured with a mean length of 22 centimeter (cm). Because of variability in the manufacturing process, the lengths of the rods are approximately normally distributed with a standard deviation of 0.06 cm. Click the icon to view a table of areas under the normal curve. (a) What proportion of rods has a length less than 21.9 cm? 0.0475 (Round to four decimal places as needed.) (b) Any rods that are shorter than 21.86 cm or longer than 22.14 cm are discarded. What proportion of rods will be discarded? (Round to four decimal places as needed.)
Transcribed Image Text:Steel rods are manufactured with a mean length of 22 centimeter (cm). Because of variability in the manufacturing process, the lengths of the rods are approximately normally distributed with a standard deviation of 0.06 cm. Click the icon to view a table of areas under the normal curve. (a) What proportion of rods has a length less than 21.9 cm? 0.0475 (Round to four decimal places as needed.) (b) Any rods that are shorter than 21.86 cm or longer than 22.14 cm are discarded. What proportion of rods will be discarded? (Round to four decimal places as needed.)
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