A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN: 9780134753119
Author: Sheldon Ross
Publisher: PEARSON
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Concept explainers

Estimation
A new framework of data analysis where the new statistical methods are used for interpreting the results and analyzing the data is known as estimation in statistics.
Question

*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
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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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