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The common fruit fly Drosophila melanogaster is the most studied organism in genetic research because it is small, is easy to grow, and reproduces rapidly. The length of the thorax (where the wings and legs attach) in a population of male fruit flies is approximately Normal with mean 0.800 millimeters (mm) and standard deviation 0.078 mm. (b) What proportion of flies have thorax length greater than 0.87 mm? (Enter your answer as a percentage rounded to two decimal places.)   proportion:     (c) What proportion of flies have a thorax of length between 0.68 mm and 0.87 mm? (Enter your answer as a percentage rounded to two decimal places.)   proportion:

The common fruit fly Drosophila melanogaster is the most studied organism in genetic research because it is small, is easy to grow, and reproduces rapidly. The length of the thorax (where the wings and legs attach) in a population of male fruit flies is approximately Normal with mean 0.800 millimeters (mm) and standard deviation 0.078 mm. (b) What proportion of flies have thorax length greater than 0.87 mm? (Enter your answer as a percentage rounded to two decimal places.)   proportion:     (c) What proportion of flies have a thorax of length between 0.68 mm and 0.87 mm? (Enter your answer as a percentage rounded to two decimal places.)   proportion:

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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The common fruit fly Drosophila melanogaster is the most studied organism in genetic research because it is small, is easy to grow, and reproduces rapidly. The length of the thorax (where the wings and legs attach) in a population of male fruit flies is approximately Normal with mean 0.800 millimeters (mm) and standard deviation 0.078 mm.

(b) What proportion of flies have thorax length greater than 0.87 mm?
(Enter your answer as a percentage rounded to two decimal places.)
 
proportion:
 
 
(c) What proportion of flies have a thorax of length between 0.68 mm and 0.87 mm? (Enter your answer as a percentage rounded to two decimal places.)
 
proportion:
696 TABLES Table entry for z is the area under the Table entry standard Normal curve to the left of z. TABLE A Standard normal cumulative proportions .00 .01 .02 .03 .04 .05 .06 .07 .08 .09 -3.4 .0003 .0003 .0003 .0003 .0003 .0003 .0003 .0003 .0003 .0002 .0003 .0005 .0007 .0005 .0004 .0006 -3.3 .0005 .0005 .0004 .0004 .0004 .0004 .0004 -3.2 .0007 .0007 .0006 .0006 .0006 .0006 .0005 .0005 -3.1 .0010 .0009 .0009 .0009 .0008 .0008 .0008 .0008 .0007 -3.0 .0013 .0013 .0013 .0012 .0012 .0011 .0011 .0011 .0010 .0010 -2.9 .0019 .0018 .0018 .0017 .0016 .0016 .0015 .0015 .0014 .0014 .0023 .0032 -2.8 .0026 .0025 .0024 .0023 .0022 .0021 .0021 .0020 .0019 -2.7 .0035 .0034 .0033 .0031 .0030 .0029 .0028 .0027 .0026 -2.6 .0047 .0045 .0044 .0043 .0041 .0040 .0054 .0039 .0038 .0037 .0036 -2.5 .0062 .0060 .0059 .0057 .0055 .0052 .0051 .0049 .0048 -2.4 .0064 .0084 .0082 .0080 .0078 .0075 .0073 .0071 .0069 .0068 .0066 -2.3 .0107 .0104 .0102 .0099 .0096 .0094 .0091 .0089 .0087 -2.2 .0139 .0136 .0132 .0129 .0125 .0122 .0119 .0116 .0113 .0110 .0174 .0222 .0170 .0217 -2.1 .0179 .0166 .0162 .0158 .0154 .0150 .0146 .0143 -2.0 .0228 .0212 .0207 .0202 .0197 .0192 .0188 .0183 .0274 .0287 .0359 .0281 .0268 .0262 .0256 .0250 .0233 .0244 .0307 .0384 -1.9 .0239 .0314 - 1.8 - 1.7 .0336 .0418 .0516 .0329 .0409 .0351 .0344 .0322 .0301 .0294 .0446 .0436 .0427 .0401 .0392 .0375 .0367 .0485 .0505 .0618 .0455 .0548 .0668 -1.6 .0537 .0526 .0495 .0475 .0465 -1.5 .0655 .0643 .0630 .0606 .0594 .0582 .0571 .0559 -1.4 -1.3 .0694 .0838 .0808 .0793 .0778 .0764 .0749 .0735 .0721 .0708 .0681 .0968 .0951 .0934 .0918 .0901 .0885 .0869 .0853 .0823 - 1.2 - 1.1 .1038 .1230 .1151 .1131 .1112 .1093 .1075 .1056 .1020 .1003 .0985 .1357 .1335 .1314 .1292 .1271 .1251 .1210 .1190 .1170 -1.0 .1587 .1562 .1539 .1515 .1492 .1469 .1446 .1423 .1401 .1379 .1814 .2090 -0.9 .1841 .1788 .1762 .1736 .1711 .1685 .1660 .1635 .1611 -0.8 .2119 .2061 .2033 .2005 .1977 .1949 .1922 .1894 .1867 -0.7 .2420 .2389 .2358 .2327 .2296 .2266 .2236 .2206 .2177 .2148 -0.6 .2743 .2709 .2676 .2643 .2611 .2578 .2546 .2514 .2483 .2451 -0.5 3085 3050 .3015 .2981 .2946 .2912 .2877 .2843 .2810 .2776 .3409 .3783 .4168 -0.4 .3446 .3372 .3336 3300 .3264 .3228 .3192 .3156 .3121 -0.3 .3821 .3745 3707 .3669 .3632 .3594 .3557 3520 .3483 .4090 .4483 .4880 -0.2 .4207 .4129 .4052 .4013 .3974 .3936 .3897 .3859 .4404 .4801 .4247 .4641 -0.1 .4602 .4562 .4522 .4443 .4364 .4325 .4286 -0.0 .5000 .4960 .4920 .4840 .4761 .4721 .4681
Transcribed Image Text:696 TABLES Table entry for z is the area under the Table entry standard Normal curve to the left of z. TABLE A Standard normal cumulative proportions .00 .01 .02 .03 .04 .05 .06 .07 .08 .09 -3.4 .0003 .0003 .0003 .0003 .0003 .0003 .0003 .0003 .0003 .0002 .0003 .0005 .0007 .0005 .0004 .0006 -3.3 .0005 .0005 .0004 .0004 .0004 .0004 .0004 -3.2 .0007 .0007 .0006 .0006 .0006 .0006 .0005 .0005 -3.1 .0010 .0009 .0009 .0009 .0008 .0008 .0008 .0008 .0007 -3.0 .0013 .0013 .0013 .0012 .0012 .0011 .0011 .0011 .0010 .0010 -2.9 .0019 .0018 .0018 .0017 .0016 .0016 .0015 .0015 .0014 .0014 .0023 .0032 -2.8 .0026 .0025 .0024 .0023 .0022 .0021 .0021 .0020 .0019 -2.7 .0035 .0034 .0033 .0031 .0030 .0029 .0028 .0027 .0026 -2.6 .0047 .0045 .0044 .0043 .0041 .0040 .0054 .0039 .0038 .0037 .0036 -2.5 .0062 .0060 .0059 .0057 .0055 .0052 .0051 .0049 .0048 -2.4 .0064 .0084 .0082 .0080 .0078 .0075 .0073 .0071 .0069 .0068 .0066 -2.3 .0107 .0104 .0102 .0099 .0096 .0094 .0091 .0089 .0087 -2.2 .0139 .0136 .0132 .0129 .0125 .0122 .0119 .0116 .0113 .0110 .0174 .0222 .0170 .0217 -2.1 .0179 .0166 .0162 .0158 .0154 .0150 .0146 .0143 -2.0 .0228 .0212 .0207 .0202 .0197 .0192 .0188 .0183 .0274 .0287 .0359 .0281 .0268 .0262 .0256 .0250 .0233 .0244 .0307 .0384 -1.9 .0239 .0314 - 1.8 - 1.7 .0336 .0418 .0516 .0329 .0409 .0351 .0344 .0322 .0301 .0294 .0446 .0436 .0427 .0401 .0392 .0375 .0367 .0485 .0505 .0618 .0455 .0548 .0668 -1.6 .0537 .0526 .0495 .0475 .0465 -1.5 .0655 .0643 .0630 .0606 .0594 .0582 .0571 .0559 -1.4 -1.3 .0694 .0838 .0808 .0793 .0778 .0764 .0749 .0735 .0721 .0708 .0681 .0968 .0951 .0934 .0918 .0901 .0885 .0869 .0853 .0823 - 1.2 - 1.1 .1038 .1230 .1151 .1131 .1112 .1093 .1075 .1056 .1020 .1003 .0985 .1357 .1335 .1314 .1292 .1271 .1251 .1210 .1190 .1170 -1.0 .1587 .1562 .1539 .1515 .1492 .1469 .1446 .1423 .1401 .1379 .1814 .2090 -0.9 .1841 .1788 .1762 .1736 .1711 .1685 .1660 .1635 .1611 -0.8 .2119 .2061 .2033 .2005 .1977 .1949 .1922 .1894 .1867 -0.7 .2420 .2389 .2358 .2327 .2296 .2266 .2236 .2206 .2177 .2148 -0.6 .2743 .2709 .2676 .2643 .2611 .2578 .2546 .2514 .2483 .2451 -0.5 3085 3050 .3015 .2981 .2946 .2912 .2877 .2843 .2810 .2776 .3409 .3783 .4168 -0.4 .3446 .3372 .3336 3300 .3264 .3228 .3192 .3156 .3121 -0.3 .3821 .3745 3707 .3669 .3632 .3594 .3557 3520 .3483 .4090 .4483 .4880 -0.2 .4207 .4129 .4052 .4013 .3974 .3936 .3897 .3859 .4404 .4801 .4247 .4641 -0.1 .4602 .4562 .4522 .4443 .4364 .4325 .4286 -0.0 .5000 .4960 .4920 .4840 .4761 .4721 .4681
TABLES 697 Table entry Table entry for z is the area under the standard Normal curve to the left of z. TABLE A Standard Normal cumulative proportions (continued) .00 .01 .02 .03 .04 .05 .06 .07 .08 .09 0.0 .5000 .5040 .5080 .5120 .5160 .5199 .5239 .5279 .5319 .5359 .5557 .5948 .6331 .5636 .6026 0.1 .5398 .5438 .5478 .5517 .5596 .5675 .5714 .5753 0.2 .5793 .5832 .5871 .5910 .5987 .6064 .6103 .6141 0.3 0.4 .6406 .6772 .6480 .6844 .6179 .6217 .6255 .6293 .6368 .6443 .6517 .6554 .6591 .6628 .6664 .6700 .6736 .6808 .6879 .6950 .7054 .7389 .7088 .7422 .7123 .7454 .7764 0.5 .6915 .6985 .7019 .7157 .7190 .7224 0.6 .7257 .7580 .7517 .7823 .8106 .7291 .7324 .7357 .7486 .7794 .8078 .8340 .7549 0.7 .7611 .7642 .7673 .7704 .7734 .7852 .8023 .8289 0.8 .7881 .7910 .7939 .7967 .7995 .8051 .8133 0.9 .8159 .8186 .8212 .8238 .8264 .8315 .8365 .8389 .8485 .8708 .8907 .8508 .8577 .8790 1.0 .8413 .8438 .8461 .8531 .8554 .8599 .8621 .8643 .8849 .8749 .8944 1.1 .8665 .8686 .8729 .8770 .8810 .8830 1.2 .8869 .8888 .8925 .8962 .8980 .8997 .9015 1.3 .9032 .9049 .9066 .9082 .9099 .9115 .9131 .9147 .9162 .9177 1.4 .9192 .9207 .9222 .9236 .9251 .9265 .9279 .9292 .9306 .9319 1.5 .9332 .9345 .9357 .9370 .9382 .9394 .9406 .9418 .9429 .9441 .9463 .9564 1.6 .9452 .9474 .9484 .9495 .9505 .9515 .9525 .9535 .9545 1.7 .9554 .9573 .9582 .9591 .9599 .9608 .9616 .9625 .9633 .9678 .9744 1.8 .9641 .9649 .9656 .9664 .9671 .9686 .9693 .9699 .9706 1.9 .9713 .9719 .9726 .9732 .9738 .9750 .9756 .9761 .9767 2.0 .9772 .9778 .9783 .9788 .9793 .9798 .9803 .9808 .9812 .9817 2.1 .9821 .9826 .9830 .9834 .9838 .9842 .9846 .9850 .9854 .9887 .9913 .9857 2.2 .9861 .9864 .9868 .9871 .9875 .9878 .9881 .9884 .9890 2.3 .9893 .9896 .9898 .9901 .9904 .9906 .9909 .9911 .9916 2.4 .9918 .9920 .9922 .9925 .9927 .9929 .9931 .9932 .9934 .9936 2.5 .9938 .9940 .9941 .9943 .9945 .9946 .9948 .9949 .9951 .9952 2.6 .9953 .9955 .9956 .9957 .9959 .9960 .9961 .9962 .9963 .9964 2.7 .9965 .9966 .9967 .9968 .9969 .9970 .9971 .9972 .9973 .9974 .9977 .9983 2.8 .9974 .9975 .9976 .9977 .9978 .9979 .9979 .9980 .9981 2.9 .9981 .9982 .9982 .9984 .9984 .9985 .9985 9986 .9986 3.0 .9987 .9987 .9987 .9988 9988 .9989 .9989 .9989 .9990 .9990 3.1 .9990 .9991 .9991 .9991 .9992 .9992 .9992 .9992 .9993 .9993 3.2 .9993 .9993 .9994 .9994 .9994 .9994 .9994 .9996 .9995 .9995 .9995 3.3 .9995 .9995 .9995 .9996 .9996 .9996 .9996 .9996 .9997 3.4 .9997 .9997 .9997 .9997 .9997 .9997 .9997 .9997 .9997 .9998
Transcribed Image Text:TABLES 697 Table entry Table entry for z is the area under the standard Normal curve to the left of z. TABLE A Standard Normal cumulative proportions (continued) .00 .01 .02 .03 .04 .05 .06 .07 .08 .09 0.0 .5000 .5040 .5080 .5120 .5160 .5199 .5239 .5279 .5319 .5359 .5557 .5948 .6331 .5636 .6026 0.1 .5398 .5438 .5478 .5517 .5596 .5675 .5714 .5753 0.2 .5793 .5832 .5871 .5910 .5987 .6064 .6103 .6141 0.3 0.4 .6406 .6772 .6480 .6844 .6179 .6217 .6255 .6293 .6368 .6443 .6517 .6554 .6591 .6628 .6664 .6700 .6736 .6808 .6879 .6950 .7054 .7389 .7088 .7422 .7123 .7454 .7764 0.5 .6915 .6985 .7019 .7157 .7190 .7224 0.6 .7257 .7580 .7517 .7823 .8106 .7291 .7324 .7357 .7486 .7794 .8078 .8340 .7549 0.7 .7611 .7642 .7673 .7704 .7734 .7852 .8023 .8289 0.8 .7881 .7910 .7939 .7967 .7995 .8051 .8133 0.9 .8159 .8186 .8212 .8238 .8264 .8315 .8365 .8389 .8485 .8708 .8907 .8508 .8577 .8790 1.0 .8413 .8438 .8461 .8531 .8554 .8599 .8621 .8643 .8849 .8749 .8944 1.1 .8665 .8686 .8729 .8770 .8810 .8830 1.2 .8869 .8888 .8925 .8962 .8980 .8997 .9015 1.3 .9032 .9049 .9066 .9082 .9099 .9115 .9131 .9147 .9162 .9177 1.4 .9192 .9207 .9222 .9236 .9251 .9265 .9279 .9292 .9306 .9319 1.5 .9332 .9345 .9357 .9370 .9382 .9394 .9406 .9418 .9429 .9441 .9463 .9564 1.6 .9452 .9474 .9484 .9495 .9505 .9515 .9525 .9535 .9545 1.7 .9554 .9573 .9582 .9591 .9599 .9608 .9616 .9625 .9633 .9678 .9744 1.8 .9641 .9649 .9656 .9664 .9671 .9686 .9693 .9699 .9706 1.9 .9713 .9719 .9726 .9732 .9738 .9750 .9756 .9761 .9767 2.0 .9772 .9778 .9783 .9788 .9793 .9798 .9803 .9808 .9812 .9817 2.1 .9821 .9826 .9830 .9834 .9838 .9842 .9846 .9850 .9854 .9887 .9913 .9857 2.2 .9861 .9864 .9868 .9871 .9875 .9878 .9881 .9884 .9890 2.3 .9893 .9896 .9898 .9901 .9904 .9906 .9909 .9911 .9916 2.4 .9918 .9920 .9922 .9925 .9927 .9929 .9931 .9932 .9934 .9936 2.5 .9938 .9940 .9941 .9943 .9945 .9946 .9948 .9949 .9951 .9952 2.6 .9953 .9955 .9956 .9957 .9959 .9960 .9961 .9962 .9963 .9964 2.7 .9965 .9966 .9967 .9968 .9969 .9970 .9971 .9972 .9973 .9974 .9977 .9983 2.8 .9974 .9975 .9976 .9977 .9978 .9979 .9979 .9980 .9981 2.9 .9981 .9982 .9982 .9984 .9984 .9985 .9985 9986 .9986 3.0 .9987 .9987 .9987 .9988 9988 .9989 .9989 .9989 .9990 .9990 3.1 .9990 .9991 .9991 .9991 .9992 .9992 .9992 .9992 .9993 .9993 3.2 .9993 .9993 .9994 .9994 .9994 .9994 .9994 .9996 .9995 .9995 .9995 3.3 .9995 .9995 .9995 .9996 .9996 .9996 .9996 .9996 .9997 3.4 .9997 .9997 .9997 .9997 .9997 .9997 .9997 .9997 .9997 .9998
Expert Solution
Step 1

Given Information : The common fruit fly Drosophila melanogaster is the most studied organism in genetic research because it is small, is easy to grow, and reproduces rapidly. The length of the thorax (where the wings and legs attach) in a population of male fruit flies is approximately Normal with mean 0.800 millimeters (mm) and standard deviation 0.078 mm.  

Define random variable X denotes length of the thorax (where the wings and legs attach) in a population of male fruit flies . 

Here, X ~> N (μ=0.8 , σ=0.078) 

(b)
 
We need to compute . The corresponding z-value needed to be computed is: 
Statistics homework question answer, step 1, image 1
Therefore, we get that 
Statistics homework question answer, step 1, image 2
 
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