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use the values on the attached table to solve problems related to normal distribution. In a country, citizens’ annual incomes are normally distributed with a mean of $20,000 and a standard deviation of $4,000. (a)  When a citizen is randomly surveyed, what is the probability that his annual income is below $17,000? (b) When 10 citizens are randomly surveyed, what is the probability that their average annual incomes are below $17,000?

use the values on the attached table to solve problems related to normal distribution. In a country, citizens’ annual incomes are normally distributed with a mean of $20,000 and a standard deviation of $4,000. (a)  When a citizen is randomly surveyed, what is the probability that his annual income is below $17,000? (b) When 10 citizens are randomly surveyed, what is the probability that their average annual incomes are below $17,000?

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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*use the values on the attached table to solve problems related
to normal distribution.

In a country, citizens’ annual incomes are normally distributed with a mean of $20,000 and a standard deviation of $4,000.
(a)  When a citizen is randomly surveyed, what is the probability that his annual income is below $17,000?
(b) When 10 citizens are randomly surveyed, what is the probability that their
average annual incomes are below $17,000?

Table of the Standard Normal Cumulative Distribution Function &(z) .09 08 .07 90 .05 .04 .03 .02 .01 .00 .00 .01 .02 .03 .04 .05 .06 .07 .08 .09 .00003 .00003 .00004 .00004 |.00004 .00004 .00004 .00004 .00005 |.00005 .00005 .00005.00005 .00006 .00006 .00006 .00006 .00007 .00007 .00007 .00008 .00008 |.00008 .00008 | .00009 .00009 .00010 .00010 .00010 |.00011 .00011 .00012.00012 .00013 .00013 .00014.00014 .00015 |.00015 |.00016 .00017 .00017 .00018 |.00019 .00019 |.00020 .00021 |.00022 .00022 |.00023 .00024 .00025.00026 .00027 .00028 .00029 .00030 .00031 .00032 .00034 .00035 .00036.00038 .00039 .00040 .00042 .00043 .00045 |.00047 .00048 .00050 .00052.00054 .00056 .00058 .00060 .00062 .00064 |.00066 .00069 .00071 .00074.00076 .00079 .00082 .00084 .00087 .00090 .00094 .00097 .00100 .00104 |.00107 .00111 |.00114 | .00118 .00122 | .00126 |.00131 |.00135 .00139 .00144.00149 .00154 .00159 .00164.00169 .00175 .00181 .00187 .00193 .00199.00205 .00212 .00219 .00226 .00233 .00240 |.00248 .00256 .00264 .00272.00280 .00289 .00298 .00307 .00317 .00326 .00336 .00347 .00357 .00368 |.00379 | .00391 |.00402 | .00415| .00427 |.00440 |.00453 .00466 .00480 .00494.00508 .00523 .00539 | .00554 .00570 |.00587 .00604 |.00621 .00639 .00657.00676 .00695 .00714 .00734.00755 |.00776 |.00798 |.00820 .00842 .00866|.00889 .00914 .00939 .00964 .00990 .01017 .01044 .01072 .01101 .01130 .01160 .01191 .01222 .01255 .01287 .01321 .01355 .01390 .01426 .01463.01500 .01539 .01578 .01618 .01659 .01700 .01743 .01786 .01831 .01876.01923 | .01970 .02018 | .02068 .02118 | .02169 | .02222 |.02275 .02330 .02385 .02442 .02500 |.02559 | .02619|.02680 |.02743 .02807 |.02872 .02938 .03005 |.03074 .03144 |.03216 | .03288 .03362 .03438 .03515 |.03593 .03673 .03754.03836 |.03920 |.04006 |.04093 .04182 |.04272 .04363 |.04457 .04551 .04648.04746 .04846 .04947 .05050 .05155 .05262 .05370 .05480 .50000 .50399.50798 .51197.51595 .51994.52392 .52790 .53188 .53586 .53983 .54380.54776 .55172 .55567 .55962.56356 .56749 .57142 .57535 .57926 .58317.58706 .59095 .59483 .59871 .60257 .60642 .61026 .61409 .61791 .62172.62552 .62930 .63307 .63683 .64058 .64431 .64803 .65173 .65542 .65910.66276 .66640 .67003 .67364 .67724 .68082 .68439 .68793 .69146 .69497 .69847|.70194.70540 |.70884.71226|.71566 | .71904 |.72240 .72575 .72907.73237 | .73565 .73891 .74215 .74537 .74857 .75175 .75490 .75804 .76115 .76424|.76730|.77035 | .77337 |.77637|.77935 |.78230 |.78524 .78814 .79103.79389 .79673 .79955 .80234 .80511 .80785 .81057 .81327 .81594 .81859 .82121 .82381 .82639 | .82894 .83147 .83398 .83646 .83891 .84134 .84375.84614 .84849 .85083 .85314 .85543 .85769 .85993 .86214 .86433 .86650 .86864 .87076 .87286 .87493 .87698 | .87900 |.88100 |.88298 .88493 .88686.88877 .89065 .89251 .89435 .89617 .89796 .89973 .90147 .90320 .90490.90658 .90824 .90988 | .91149 | .91309 .91466 .91621 | .91774 .91924 .9207392220 | .92364 |.92507| .92647 | .92785 | .92922 | .93056 | .93189 .93319 .93448 .93574 .93699 |.93822| .93943 .94062 | .94179 | .94295 |.94408 .94520 .94630.94738 .94845 .94950 95053 .95154 .95254 .95352 .95449 .95543 .95637|.95728| .95818 | .95907| .95994 |.96080 .96164 |.96246 |.96327 .96407 .96485.96562 .96638 .96712 .96784 .96856 96926 96995 .97062 .97128 .97193 .97257 .97320|.97381| .97441.97500 | .97558 .97615 |.97670 .97725 .97778.97831 .97882 .97932 97982 .98030 98077 98124 .98169 .98214 .98257 .98300 .98341 .98382 .98422 .98461 |.98500 |.98537 |.98574 98610 .9864598679 .98713 .98745 .98778 98809 .98840 98870 .98899 .98928 98956.98983 | .99010 |.99036 | .99061 | .99086 | .99111 |.99134 | .99158 .99180 .99202 .99224 .99245 .99266 .99286 .99305 .99324 .99343 .99361 .99379 .99396.99413 .99430 .99446 .99461 .99477 .99492 .99506 .99520 .99534 .99547.99560 .99573 .99585 .99598 .99609 |.99621 | .99632 |.99643 .99653 .99664 .99674 .99683 .99693 .99702 .99711 .99720 .99728 .99736 99744 9975299760 99767 .99774 .99781 .99788 .99795 .99801 .99807 .99813 .99819.99825 .99831 .99836 .99841 .99846 99851 .99856 .99861 99865 9986999874 .99878 .99882 |.99886 .99889 | .99893 |.99896 |.99900 .99903 .99906.99910 .99913 .99916 .99918 .99921 .99924 .99926 .99929 .99931 .99934.99936 .99938 .99940 .99942 .99944 .99946 .99948 .99950 .99952 .99953 .99955 .99957 .99958| .99960 |.99961|.99962 .99964 .99965 .99966 .99968.99969 .99970 .99971 .99972 .99973 .99974 .99975 .99976 .99977 .99978.99978 .99979 .99980 .99981 .99981 | .99982 .99983 .99983 .99984 .99985.99985 .99986 .99986 .99987 .99987 .99988 .99988 .99989 .99989 .99990 .99990 .99990 .99991|.99991.99992 | .99992 .99992 |.99992 .99993 .99993.99993 .99994 .99994 99994 .99994 99995 99995 .99995 .99995 .99995|.99996 | .99996 |.99996 | .99996 | .99996 | .99996 | .99997 | .99997 -3.9 0.0 -3.8 0.1 -3.7 0.2 -3.6 0.3 -3.5 0.4 -3.4 0.5 -3.3 0.6 -3.2 0.7 -3.1 0.8 -3.0 0.9 -2.9 1.0 -2.8 1.1 -2.7 1.2 -2.6 1.3 -2.5 1.4 -2.4 1.5 -2.3 1.6 -2.2 1.7 -2.1 1.8 -2.0 1.9 -1.9 2.0 -1.8 2.1 -1.7 2.2 -1.6 .05592 .05705.05821 .05938 .06057 .06178 .06301 .06426 .06552 .06681 .06811 .06944.07078 .07215 .07353 | .07493 .07636 |.07780 |.07927 |.08076 .08226 .08379.08534 .08691 .08851 .09012 .09176 .09342 .09510 .09680 .09853 .10027.10204 |.10383 .10565 .10749 |.10935 |.11123 |.11314 |.11507 .11702 .11900.12100 |.12302|.12507 |.12714.12924 |.13136 .13350 |.13567 .13786 .14007.14231 |.14457.14686 .14917 .15151 |.15386 .15625 .15866 .16109|.16354.16602 .16853.17106 .17361.17619 .17879 .18141 .18406 .18673 | .18943 |.19215|.19489.19766 | .20045 .20327|.20611 .20897|.21186 .21476 .21770 .22065 .22363 .22663 .22965 .23270 .23576 .23885 .24196 .24510 .24825.25143 .25463 .25785 .26109 .26435 .26763| .27093 | .27425 .27760 .28096 .28434 |.28774| .29116 |.29460 .29806 .30153 | .30503 | .30854 .31207 .31561|.31918| .32276 |.32636|.32997.33360 |.33724 .34090 |.34458 .34827 .35197|.35569 .35942.36317|.36693 .37070 .37448 .37828| .38209 .38591 .38974| .39358 | .39743 | .40129 | .40517 | .40905 | .41294 | .41683 .42074 .42465 .42858| 43251 | .43644 |.44038 | .44433 44828 .45224 .45620 | .46017 .46414 .46812 47210| .47608 .48006 | .48405 | .48803 | .49202 | .49601 .50000 2.3 -1.5 2.4 -1.4 2.5 -1.3 2.6 -1.2 2.7 -1.1 2.8 -1.0 2.9 -0.9 3.0 -0.8 3.1 -0.7 3.2 -0.6 3.3 -0.5 3.4 -0.4 3.5 -0.3 3.6 -0.2 3.7 -0.1 3.8 -0.0 3.9
Transcribed Image Text:Table of the Standard Normal Cumulative Distribution Function &(z) .09 08 .07 90 .05 .04 .03 .02 .01 .00 .00 .01 .02 .03 .04 .05 .06 .07 .08 .09 .00003 .00003 .00004 .00004 |.00004 .00004 .00004 .00004 .00005 |.00005 .00005 .00005.00005 .00006 .00006 .00006 .00006 .00007 .00007 .00007 .00008 .00008 |.00008 .00008 | .00009 .00009 .00010 .00010 .00010 |.00011 .00011 .00012.00012 .00013 .00013 .00014.00014 .00015 |.00015 |.00016 .00017 .00017 .00018 |.00019 .00019 |.00020 .00021 |.00022 .00022 |.00023 .00024 .00025.00026 .00027 .00028 .00029 .00030 .00031 .00032 .00034 .00035 .00036.00038 .00039 .00040 .00042 .00043 .00045 |.00047 .00048 .00050 .00052.00054 .00056 .00058 .00060 .00062 .00064 |.00066 .00069 .00071 .00074.00076 .00079 .00082 .00084 .00087 .00090 .00094 .00097 .00100 .00104 |.00107 .00111 |.00114 | .00118 .00122 | .00126 |.00131 |.00135 .00139 .00144.00149 .00154 .00159 .00164.00169 .00175 .00181 .00187 .00193 .00199.00205 .00212 .00219 .00226 .00233 .00240 |.00248 .00256 .00264 .00272.00280 .00289 .00298 .00307 .00317 .00326 .00336 .00347 .00357 .00368 |.00379 | .00391 |.00402 | .00415| .00427 |.00440 |.00453 .00466 .00480 .00494.00508 .00523 .00539 | .00554 .00570 |.00587 .00604 |.00621 .00639 .00657.00676 .00695 .00714 .00734.00755 |.00776 |.00798 |.00820 .00842 .00866|.00889 .00914 .00939 .00964 .00990 .01017 .01044 .01072 .01101 .01130 .01160 .01191 .01222 .01255 .01287 .01321 .01355 .01390 .01426 .01463.01500 .01539 .01578 .01618 .01659 .01700 .01743 .01786 .01831 .01876.01923 | .01970 .02018 | .02068 .02118 | .02169 | .02222 |.02275 .02330 .02385 .02442 .02500 |.02559 | .02619|.02680 |.02743 .02807 |.02872 .02938 .03005 |.03074 .03144 |.03216 | .03288 .03362 .03438 .03515 |.03593 .03673 .03754.03836 |.03920 |.04006 |.04093 .04182 |.04272 .04363 |.04457 .04551 .04648.04746 .04846 .04947 .05050 .05155 .05262 .05370 .05480 .50000 .50399.50798 .51197.51595 .51994.52392 .52790 .53188 .53586 .53983 .54380.54776 .55172 .55567 .55962.56356 .56749 .57142 .57535 .57926 .58317.58706 .59095 .59483 .59871 .60257 .60642 .61026 .61409 .61791 .62172.62552 .62930 .63307 .63683 .64058 .64431 .64803 .65173 .65542 .65910.66276 .66640 .67003 .67364 .67724 .68082 .68439 .68793 .69146 .69497 .69847|.70194.70540 |.70884.71226|.71566 | .71904 |.72240 .72575 .72907.73237 | .73565 .73891 .74215 .74537 .74857 .75175 .75490 .75804 .76115 .76424|.76730|.77035 | .77337 |.77637|.77935 |.78230 |.78524 .78814 .79103.79389 .79673 .79955 .80234 .80511 .80785 .81057 .81327 .81594 .81859 .82121 .82381 .82639 | .82894 .83147 .83398 .83646 .83891 .84134 .84375.84614 .84849 .85083 .85314 .85543 .85769 .85993 .86214 .86433 .86650 .86864 .87076 .87286 .87493 .87698 | .87900 |.88100 |.88298 .88493 .88686.88877 .89065 .89251 .89435 .89617 .89796 .89973 .90147 .90320 .90490.90658 .90824 .90988 | .91149 | .91309 .91466 .91621 | .91774 .91924 .9207392220 | .92364 |.92507| .92647 | .92785 | .92922 | .93056 | .93189 .93319 .93448 .93574 .93699 |.93822| .93943 .94062 | .94179 | .94295 |.94408 .94520 .94630.94738 .94845 .94950 95053 .95154 .95254 .95352 .95449 .95543 .95637|.95728| .95818 | .95907| .95994 |.96080 .96164 |.96246 |.96327 .96407 .96485.96562 .96638 .96712 .96784 .96856 96926 96995 .97062 .97128 .97193 .97257 .97320|.97381| .97441.97500 | .97558 .97615 |.97670 .97725 .97778.97831 .97882 .97932 97982 .98030 98077 98124 .98169 .98214 .98257 .98300 .98341 .98382 .98422 .98461 |.98500 |.98537 |.98574 98610 .9864598679 .98713 .98745 .98778 98809 .98840 98870 .98899 .98928 98956.98983 | .99010 |.99036 | .99061 | .99086 | .99111 |.99134 | .99158 .99180 .99202 .99224 .99245 .99266 .99286 .99305 .99324 .99343 .99361 .99379 .99396.99413 .99430 .99446 .99461 .99477 .99492 .99506 .99520 .99534 .99547.99560 .99573 .99585 .99598 .99609 |.99621 | .99632 |.99643 .99653 .99664 .99674 .99683 .99693 .99702 .99711 .99720 .99728 .99736 99744 9975299760 99767 .99774 .99781 .99788 .99795 .99801 .99807 .99813 .99819.99825 .99831 .99836 .99841 .99846 99851 .99856 .99861 99865 9986999874 .99878 .99882 |.99886 .99889 | .99893 |.99896 |.99900 .99903 .99906.99910 .99913 .99916 .99918 .99921 .99924 .99926 .99929 .99931 .99934.99936 .99938 .99940 .99942 .99944 .99946 .99948 .99950 .99952 .99953 .99955 .99957 .99958| .99960 |.99961|.99962 .99964 .99965 .99966 .99968.99969 .99970 .99971 .99972 .99973 .99974 .99975 .99976 .99977 .99978.99978 .99979 .99980 .99981 .99981 | .99982 .99983 .99983 .99984 .99985.99985 .99986 .99986 .99987 .99987 .99988 .99988 .99989 .99989 .99990 .99990 .99990 .99991|.99991.99992 | .99992 .99992 |.99992 .99993 .99993.99993 .99994 .99994 99994 .99994 99995 99995 .99995 .99995 .99995|.99996 | .99996 |.99996 | .99996 | .99996 | .99996 | .99997 | .99997 -3.9 0.0 -3.8 0.1 -3.7 0.2 -3.6 0.3 -3.5 0.4 -3.4 0.5 -3.3 0.6 -3.2 0.7 -3.1 0.8 -3.0 0.9 -2.9 1.0 -2.8 1.1 -2.7 1.2 -2.6 1.3 -2.5 1.4 -2.4 1.5 -2.3 1.6 -2.2 1.7 -2.1 1.8 -2.0 1.9 -1.9 2.0 -1.8 2.1 -1.7 2.2 -1.6 .05592 .05705.05821 .05938 .06057 .06178 .06301 .06426 .06552 .06681 .06811 .06944.07078 .07215 .07353 | .07493 .07636 |.07780 |.07927 |.08076 .08226 .08379.08534 .08691 .08851 .09012 .09176 .09342 .09510 .09680 .09853 .10027.10204 |.10383 .10565 .10749 |.10935 |.11123 |.11314 |.11507 .11702 .11900.12100 |.12302|.12507 |.12714.12924 |.13136 .13350 |.13567 .13786 .14007.14231 |.14457.14686 .14917 .15151 |.15386 .15625 .15866 .16109|.16354.16602 .16853.17106 .17361.17619 .17879 .18141 .18406 .18673 | .18943 |.19215|.19489.19766 | .20045 .20327|.20611 .20897|.21186 .21476 .21770 .22065 .22363 .22663 .22965 .23270 .23576 .23885 .24196 .24510 .24825.25143 .25463 .25785 .26109 .26435 .26763| .27093 | .27425 .27760 .28096 .28434 |.28774| .29116 |.29460 .29806 .30153 | .30503 | .30854 .31207 .31561|.31918| .32276 |.32636|.32997.33360 |.33724 .34090 |.34458 .34827 .35197|.35569 .35942.36317|.36693 .37070 .37448 .37828| .38209 .38591 .38974| .39358 | .39743 | .40129 | .40517 | .40905 | .41294 | .41683 .42074 .42465 .42858| 43251 | .43644 |.44038 | .44433 44828 .45224 .45620 | .46017 .46414 .46812 47210| .47608 .48006 | .48405 | .48803 | .49202 | .49601 .50000 2.3 -1.5 2.4 -1.4 2.5 -1.3 2.6 -1.2 2.7 -1.1 2.8 -1.0 2.9 -0.9 3.0 -0.8 3.1 -0.7 3.2 -0.6 3.3 -0.5 3.4 -0.4 3.5 -0.3 3.6 -0.2 3.7 -0.1 3.8 -0.0 3.9
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