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Q1) The following are the share prices ($) of some companies: 23, 45, 26, 30 and 35. a) What is the name of the variable? b) Calculate skewness. Which formula is used to calculate the skewness of the above set of data? Write this formula. c) Comment about the shape of the distribution whether the given variable is right skewed or left skewed.

Q1) The following are the share prices ($) of some companies: 23, 45, 26, 30 and 35. a) What is the name of the variable? b) Calculate skewness. Which formula is used to calculate the skewness of the above set of data? Write this formula. c) Comment about the shape of the distribution whether the given variable is right skewed or left skewed.

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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Q1) The following are the share prices ($) of some companies: 23, 45, 26, 30 and 35.

a) What is the name of the variable?

b) Calculate skewness. Which formula is used to calculate the skewness of the above set of data? Write this formula.

c) Comment about the shape of the distribution whether the given variable is right skewed or left skewed.

d) Write a summary based on your result.

 

Notes_210906_110307 (1) (1).pdf 2 | 3 | 100% + | CUMULATIVE PROBABILITIES FOR THE STANDARD NORMAL DISTRIBUTION Cumulative Entries in the table probability give the area under the curve to the left of the z value. For example, for z= 1.25, the cumulative probability is .8944. .00 .01 .02 .03 .04 .05 .06 .07 .08 .09 5000 5040 5080 5120 .5160 5199 5239 5359 5753 .6141 .0 5279 5319 5398 .2 .5793 .6179 .5438 .5832 .6217 .5478 .5871 5517 5910 6293 5557 .5948 .6331 .5596 5636 .5675 5714 5987 .6026 .6064 .6103 .3 .6255 .6368 6406 .6443 .6480 .6517 .4 .6554 .6591 .6628 .6664 .6700 .6736 .6772 .6808 .6844 .6879 .5 .6915 .7257 .6950 .6985 7019 .7054 .7088 .7123 .7157 .7190 7224 .6 .7291 .7324 .7357 .7389 7422 7454 ,7486 .7517 .7549 .7580 .7881 .7 .7611 .7910 .7823 .7852 .8133 8389 .7642 .7673 .7704 .7734 .7764 .7794 7939 .7967 .7995 .8078 .8340 .8 .8023 .8289 8051 .8106 8365 8159 .8186 .8212 .8238 .8264 8315 1.0 .8413 .8643 .8438 .8665 .8485 .8708 .8508 .8531 .8749 8944 9115 8461 8554 .8577 8599 .8621 .8729 8925 1.1 .8686 .8770 .8790 .8810 .8830 .8888 .9066 .9222 1.2 8849 8869 .8907 .8980 .8962 9131 .9279 .8997 9015 9049 .9207 1.3 .9082 .9032 .9192 9099 9251 .9147 9292 .9162 .9306 9177 1.4 9236 9265 .9319 .9345 9463 1.5 .9332 .9357 .9370 .9382 .9394 9406 9418 .9429 9441 .9452 9554 .9484 9582 .9664 .9505 9599 .9495 .9525 9616 .9693 1.6 .9474 .9515 .9535 .9545 .9564 .9649 .9719 9573 .9656 9591 .9671 .9738 .9633 .9706 1.7 .9608 .9625 1.8 .9641 .9678 .9686 .9699 1.9 .9713 9726 .9732 9744 .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 .9857 2.2 .9861 .9864 9871 9875 .9878 .9906 .9868 .9881 9884 9887 .9890 2.3 .9893 .9896 .9898 .9901 .9925 .9904 .9909 .9911 .9913 .9916 2.4 .9918 .9920 .9922 9927 .9929 .9931 9932 .9934 .9936 .9941 .9956 .9943 .9945 .9951 .9963 2.5 .9938 .9940 .9946 .9948 .9949 .9952 2.6 9953 9955 .9957 .9959 .9961 .9962 9972 9960 .9964 .9965 .9974 .9968 .9977 .9969 .9970 .9973 9980 2.7 .9966 .9967 .9971 .9974 2.8 .9975 .9976 .9977 .9978 .9979 .9979 .9981 2.9 9981 .9982 .9982 .9983 .9984 .9984 9985 9985 9986 9986 3.0 .9987 9987 .9987 .9988 .9988 .9989 .9989 .9989 .9990 .9990 II
Transcribed Image Text:Notes_210906_110307 (1) (1).pdf 2 | 3 | 100% + | CUMULATIVE PROBABILITIES FOR THE STANDARD NORMAL DISTRIBUTION Cumulative Entries in the table probability give the area under the curve to the left of the z value. For example, for z= 1.25, the cumulative probability is .8944. .00 .01 .02 .03 .04 .05 .06 .07 .08 .09 5000 5040 5080 5120 .5160 5199 5239 5359 5753 .6141 .0 5279 5319 5398 .2 .5793 .6179 .5438 .5832 .6217 .5478 .5871 5517 5910 6293 5557 .5948 .6331 .5596 5636 .5675 5714 5987 .6026 .6064 .6103 .3 .6255 .6368 6406 .6443 .6480 .6517 .4 .6554 .6591 .6628 .6664 .6700 .6736 .6772 .6808 .6844 .6879 .5 .6915 .7257 .6950 .6985 7019 .7054 .7088 .7123 .7157 .7190 7224 .6 .7291 .7324 .7357 .7389 7422 7454 ,7486 .7517 .7549 .7580 .7881 .7 .7611 .7910 .7823 .7852 .8133 8389 .7642 .7673 .7704 .7734 .7764 .7794 7939 .7967 .7995 .8078 .8340 .8 .8023 .8289 8051 .8106 8365 8159 .8186 .8212 .8238 .8264 8315 1.0 .8413 .8643 .8438 .8665 .8485 .8708 .8508 .8531 .8749 8944 9115 8461 8554 .8577 8599 .8621 .8729 8925 1.1 .8686 .8770 .8790 .8810 .8830 .8888 .9066 .9222 1.2 8849 8869 .8907 .8980 .8962 9131 .9279 .8997 9015 9049 .9207 1.3 .9082 .9032 .9192 9099 9251 .9147 9292 .9162 .9306 9177 1.4 9236 9265 .9319 .9345 9463 1.5 .9332 .9357 .9370 .9382 .9394 9406 9418 .9429 9441 .9452 9554 .9484 9582 .9664 .9505 9599 .9495 .9525 9616 .9693 1.6 .9474 .9515 .9535 .9545 .9564 .9649 .9719 9573 .9656 9591 .9671 .9738 .9633 .9706 1.7 .9608 .9625 1.8 .9641 .9678 .9686 .9699 1.9 .9713 9726 .9732 9744 .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 .9857 2.2 .9861 .9864 9871 9875 .9878 .9906 .9868 .9881 9884 9887 .9890 2.3 .9893 .9896 .9898 .9901 .9925 .9904 .9909 .9911 .9913 .9916 2.4 .9918 .9920 .9922 9927 .9929 .9931 9932 .9934 .9936 .9941 .9956 .9943 .9945 .9951 .9963 2.5 .9938 .9940 .9946 .9948 .9949 .9952 2.6 9953 9955 .9957 .9959 .9961 .9962 9972 9960 .9964 .9965 .9974 .9968 .9977 .9969 .9970 .9973 9980 2.7 .9966 .9967 .9971 .9974 2.8 .9975 .9976 .9977 .9978 .9979 .9979 .9981 2.9 9981 .9982 .9982 .9983 .9984 .9984 9985 9985 9986 9986 3.0 .9987 9987 .9987 .9988 .9988 .9989 .9989 .9989 .9990 .9990 II
Notes_210906_110307 (1).pdf 3 / 3 88% + Table entry for p and C is the critical value t with probability p lying to its right and probability C lying between -t' and t'. Probability p TABLE D t distribution critical values Upper-lail probability p di .25 .15 .10 .05 .025 .02 .01 .005 .0025 001 .0005 1.000 0.816 1.376 1,061 0.978 0.941 1.963 1.386 1.250 1.190 3.078 1.886 1,638 1.533 6.314 2.920 2.353 12.71 4,303 15.89 4.849 3.482 2.999 2.757 31.82 6.965 4.541 3.747 63.66 9.925 5.841 4.604 4.032 3.707 127,3 14.09 7.453 5.598 318.3 22.33 636.6 31.60 3 0.765 0.741 0.727 0.718 0.711 0.706 0.703 3.182 2.776 2.571 10.21 7.173 5.893 12.92 8.610 6.869 5.959 5,408 4 2.132 2.015 0.920 0.906 0.896 1.156 1.134 1.476 1.440 1.415 1.397 1.383 1,372 3.365 3.143 2.998 2.896 4.773 1.943 1.895 1.860 1.833 2.447 2.365 2.306 2.262 2.612 2.517 2.449 4.317 4,029 5.208 4.785 1.119 1.108 1.100 3.499 3.355 3.250 0.889 3.833 3.690 3.581 3.497 4.501 4.297 5.041 0.883 0.879 2.398 2.359 2.821 2.764 2.718 2.681 2.650 2.624 2.602 2.583 4.781 4.587 10 0.700 0.697 0.695 1.093 1.088 1.083 1.079 1.076 1.074 1.071 1.812 2.228 2.201 2.179 2.160 2.145 2.131 2.120 3.169 3.106 3.055 11 4.144 0.876 0.873 0.870 0.868 0.866 0.865 0.863 0.862 0.861 1.363 1.356 1.350 1.345 1.341 1.337 1.796 2.328 2.303 2.282 2.264 2.249 2.235 2.224 4.025 12 13 14 15 1.782 1.771 1.761 4.437 4.318 4.221 4.140 4.073 3.428 0.694 0.692 0.691 0.690 3.012 2.977 2.947 2.921 2,898 3.372 3.326 3.286 3.252 3.222 3.930 3.852 3.787 3.733 1.753 16 1.746 3.686 3.646 3.611 3.579 17 4.015 0.689 0.688 0.688 0.687 0.686 0.686 1.069 1.067 1.066 1.333 1.330 1.328 1.325 1.323 1.740 1.734 1.729 1,725 1,721 1,717 2.110 2.101 2.093 2.086 2.567 2.552 2.539 2.528 2.518 2.508 2.500 3.965 18 19 20 21 22 2.214 2.205 2,197 2,189 2.183 2.878 2.861 2.845 2.831 2.819 2.807 2.797 2.787 2.779 2.771 2.763 2.756 2.750 2.704 2.678 2.660 2.639 2.626 2.581 3.197 3.174 3.153 3.135 3.119 3.922 3.883 0.860 0.859 0.858 1.064 3.552 3,527 3.850 3.819 1.063 1.061 1.060 1.059 2.080 1.321 1.319 2.074 23 24 25 26 27 28 29 3.505 3.485 3.467 3.792 3.768 3.745 3.725 0.685 0.685 0.684 0.684 0.684 0.683 0.683 0.683 0.681 0.679 0.679 0.678 0.677 0.675 0.674 0.858 0.857 1.714 1.711 2.069 2.064 2.060 2.056 2.052 2.048 2.177 2.172 2.167 2.162 2.158 2.154 3.104 1.318 2.492 2.485 2.479 2.473 2.467 3.091 3.078 3.067 3.057 3.047 0.856 1.058 1.058 1.057 1.056 1.316 1,708 1.706 1.703 3.450 0.856 0.855 0.855 0.854 1.315 3.435 3.421 3.408 3.396 3.385 3.707 3.690 3.674 1.314 1.313 1.311 1.310 1.303 1.299 1.296 1.292 1.701 1.699 1.697 1.055 2.045 2.042 2.021 2.009 2.000 1.990 30 40 50 60 80 0.854 0.851 0.849 0.848 0.846 0.845 1.050 1.047 1.045 1.043 2.150 2.147 2.462 2.457 3.038 3.030 3.659 3.646 3.551 1.684 2.123 2.109 2.099 2.088 2.081 2.423 2.403 2.390 2.374 2.364 2.971 3.307 1.676 1,671 2937 3.261 3.496 3.460 2.915 2.887 2.871 3.232 3.195 1.664 3.416 3.390 3.300 3.291 100 1.042 1.037 1.036 1.290 1.282 1.282 1.660 1.646 1.645 1.984 3.174 3.098 3.091 1000 0,842 0.841 1.962 2.056 2.054 2.330 2.326 2.813 2.807 1.960 2.576 50% 60%% 70%% 80% 90% 95% 96% 98% 99% 99.5% 99.8% 99.9% Confidence level C II
Transcribed Image Text:Notes_210906_110307 (1).pdf 3 / 3 88% + Table entry for p and C is the critical value t with probability p lying to its right and probability C lying between -t' and t'. Probability p TABLE D t distribution critical values Upper-lail probability p di .25 .15 .10 .05 .025 .02 .01 .005 .0025 001 .0005 1.000 0.816 1.376 1,061 0.978 0.941 1.963 1.386 1.250 1.190 3.078 1.886 1,638 1.533 6.314 2.920 2.353 12.71 4,303 15.89 4.849 3.482 2.999 2.757 31.82 6.965 4.541 3.747 63.66 9.925 5.841 4.604 4.032 3.707 127,3 14.09 7.453 5.598 318.3 22.33 636.6 31.60 3 0.765 0.741 0.727 0.718 0.711 0.706 0.703 3.182 2.776 2.571 10.21 7.173 5.893 12.92 8.610 6.869 5.959 5,408 4 2.132 2.015 0.920 0.906 0.896 1.156 1.134 1.476 1.440 1.415 1.397 1.383 1,372 3.365 3.143 2.998 2.896 4.773 1.943 1.895 1.860 1.833 2.447 2.365 2.306 2.262 2.612 2.517 2.449 4.317 4,029 5.208 4.785 1.119 1.108 1.100 3.499 3.355 3.250 0.889 3.833 3.690 3.581 3.497 4.501 4.297 5.041 0.883 0.879 2.398 2.359 2.821 2.764 2.718 2.681 2.650 2.624 2.602 2.583 4.781 4.587 10 0.700 0.697 0.695 1.093 1.088 1.083 1.079 1.076 1.074 1.071 1.812 2.228 2.201 2.179 2.160 2.145 2.131 2.120 3.169 3.106 3.055 11 4.144 0.876 0.873 0.870 0.868 0.866 0.865 0.863 0.862 0.861 1.363 1.356 1.350 1.345 1.341 1.337 1.796 2.328 2.303 2.282 2.264 2.249 2.235 2.224 4.025 12 13 14 15 1.782 1.771 1.761 4.437 4.318 4.221 4.140 4.073 3.428 0.694 0.692 0.691 0.690 3.012 2.977 2.947 2.921 2,898 3.372 3.326 3.286 3.252 3.222 3.930 3.852 3.787 3.733 1.753 16 1.746 3.686 3.646 3.611 3.579 17 4.015 0.689 0.688 0.688 0.687 0.686 0.686 1.069 1.067 1.066 1.333 1.330 1.328 1.325 1.323 1.740 1.734 1.729 1,725 1,721 1,717 2.110 2.101 2.093 2.086 2.567 2.552 2.539 2.528 2.518 2.508 2.500 3.965 18 19 20 21 22 2.214 2.205 2,197 2,189 2.183 2.878 2.861 2.845 2.831 2.819 2.807 2.797 2.787 2.779 2.771 2.763 2.756 2.750 2.704 2.678 2.660 2.639 2.626 2.581 3.197 3.174 3.153 3.135 3.119 3.922 3.883 0.860 0.859 0.858 1.064 3.552 3,527 3.850 3.819 1.063 1.061 1.060 1.059 2.080 1.321 1.319 2.074 23 24 25 26 27 28 29 3.505 3.485 3.467 3.792 3.768 3.745 3.725 0.685 0.685 0.684 0.684 0.684 0.683 0.683 0.683 0.681 0.679 0.679 0.678 0.677 0.675 0.674 0.858 0.857 1.714 1.711 2.069 2.064 2.060 2.056 2.052 2.048 2.177 2.172 2.167 2.162 2.158 2.154 3.104 1.318 2.492 2.485 2.479 2.473 2.467 3.091 3.078 3.067 3.057 3.047 0.856 1.058 1.058 1.057 1.056 1.316 1,708 1.706 1.703 3.450 0.856 0.855 0.855 0.854 1.315 3.435 3.421 3.408 3.396 3.385 3.707 3.690 3.674 1.314 1.313 1.311 1.310 1.303 1.299 1.296 1.292 1.701 1.699 1.697 1.055 2.045 2.042 2.021 2.009 2.000 1.990 30 40 50 60 80 0.854 0.851 0.849 0.848 0.846 0.845 1.050 1.047 1.045 1.043 2.150 2.147 2.462 2.457 3.038 3.030 3.659 3.646 3.551 1.684 2.123 2.109 2.099 2.088 2.081 2.423 2.403 2.390 2.374 2.364 2.971 3.307 1.676 1,671 2937 3.261 3.496 3.460 2.915 2.887 2.871 3.232 3.195 1.664 3.416 3.390 3.300 3.291 100 1.042 1.037 1.036 1.290 1.282 1.282 1.660 1.646 1.645 1.984 3.174 3.098 3.091 1000 0,842 0.841 1.962 2.056 2.054 2.330 2.326 2.813 2.807 1.960 2.576 50% 60%% 70%% 80% 90% 95% 96% 98% 99% 99.5% 99.8% 99.9% Confidence level C II
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