Q4. A type of chocolate bar contains, with probability 0.1, a prize voucher. Whether or not a bar contains a voucher is independent of other bars. A hungry student buys 8 chocolate bars. Let X denote the number of vouchers that she finds. (a) What is the distribution of X? How likely is it that the student finds no vouchers? (b) Calculate the expected number of vouchers that she will find and also find the standard deviation. (e) How likely is it that she finds at least two vouchers?

MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
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Q4.
A type of chocolate bar contains, with probability 0.1, a prize voucher. Whether or not a bar
contains a voucher is independent of other bars. A hungry student buys 8 chocolate bars. Let X denote the
number of vouchers that she finds.
(a) What is the distribution of X? How likely is it that the student finds no vouchers?
(b) Calculate the expected number of vouchers that she will find and also find the standard deviation.
(e) How likely is it that she finds at least two vouchers?
STANDARD NORMAL DISTRIBUTION: Table Values Represent AREA to the LEFT of the Z score.
Z
.06
.07
.08
00004 .00003
.00004
00006
.00005
00005
00008 .00008 00008
.00
.01
.02
.03
.04
.05
-3.9 00005 00005 00004 00004 00004 .00004
-3.8 .00007 00007 00007 00006 .00006 .00006
-3.7 00011 .00010 00010 .00010 00009 .00009
-3.6 00016 .00015 00015 .00014 00014 .00013 .00013 00012 00012
-3.5 .00023 .00022 .00022 .00021 00020 .00019 00019 00018 00017
00034 00032 .00031 00030
.00029 .00028 .00027 .00026 00025
00048 00047 00045 .00043 00042 .000-40 .00039 .00038 00036
-3.2 .00069 .00066 .00064 .00062 00060 .00058 .00056 .00054 00052
-3.1 .00097 .00094 .00090 .00087 00084 .00082 .00079 .00076
00074
-3.0 00135 .00131 00126 00122 00118 .00114 00111 00107 00104
-2.9 00187 .00181 .00175 .00169 .00164 .00159
.00154 .00149 00144
-2.8 00256 .00248 00240 00233 00226 00219 00212 00205 .00199
-2.7 .00347 00336 .00326 00317 00307 .00298 .00289 00280 00272
-2.6 00466 00453 00440 00427 00415 00402 00391 00379 00368
-2.5 00621 00604 00587 00570 00554 00539 .00-23 00508 00494
-2.4 .00820 .00798 .00776 .00755 .00734 .00714 .00695 .00676 00657
-2.3 01072 01044 01017 00990 00964 .00939 .00914 .00889 00866
01390 01355 01321 01287 01255 01222 01191 .01160 01130
-2.1 01786 01743 01700 01659 01618 01578 01539 01500 01463
-2.0 02275 02222 02169 02118 02068 02018 01970 01923 01876
-1.9 02872 02807 02743 02680 02619 .02559 02500 02442 02385
-1.8 03593 03515 03438 03362 03288 03216
03144
03074 03005
-1.7 04457 04363 04272 04182 04093
04006 03920
-1.6 05480 .05370 05262 05155 05050 04947 04846
-1.5 06681 06552 06426 06301 06178 06057 05938
-1.4 08076 07927 07780 .07636 07493 07353 07215
.06811
-1.3 09680 09510 09342 09176 09012 08851 08691 08534 08379
08226
-1.2 11507 11314 11123 .10935 .10749 .10565 .10383 .10204 .10027 .09853
-1.1 .13567 13350 .13136 12924 12714 12507 12302 .12100 11900 11702
-1.0
15866
15625 15386 15151 14917 .14686
14457 .14231 14007 13786
03836 03754
03673
04746 04648
04551
05821 05705
05592
07078 06944
Appendix
-0.9 18406
-0.8 21186
.18141
20897
-0.7 24196 23885
.26435
-0.6 27425 27093
-0.5 30854 30503
-0.4
.30153
29806
34458 .34090
.33724
.33360
-0.3
37828
.37448 .37070
-0.2
41683
41294 40905
-0.1 46017 45620 45224 .44828
-0.0 50000 49601 49202
38209
42074
.17879 .17619
20611 20327
23576 23270
26763
.17106
.19766
22965
.22663
26109 25785
29460 29116
.32636
.17361
20045
32997
.36693
40517
44433
48803 48405 48006
.36317
40129
.44038
16853
.19489
.09
.00003
.00005
.00008
.00011
.00017
.00024
.00035
.00050
.00071
00100
.00139
.00193
00264
00357
.00480
.00639
00842
01101
.01426
01831
02330
02938
.16109
.16602 .16354
.19215 .18943 .18673
22363
.22065 21770 .21476
24510
25463 25143 24825
28774 28434 28096
27760
32276 31918 31561
.31207
35942 .35569
35197
.34827
39743 39358
38974
38591
42858 42465
43644 43251
47608 47210 46812 46414
Transcribed Image Text:Q4. A type of chocolate bar contains, with probability 0.1, a prize voucher. Whether or not a bar contains a voucher is independent of other bars. A hungry student buys 8 chocolate bars. Let X denote the number of vouchers that she finds. (a) What is the distribution of X? How likely is it that the student finds no vouchers? (b) Calculate the expected number of vouchers that she will find and also find the standard deviation. (e) How likely is it that she finds at least two vouchers? STANDARD NORMAL DISTRIBUTION: Table Values Represent AREA to the LEFT of the Z score. Z .06 .07 .08 00004 .00003 .00004 00006 .00005 00005 00008 .00008 00008 .00 .01 .02 .03 .04 .05 -3.9 00005 00005 00004 00004 00004 .00004 -3.8 .00007 00007 00007 00006 .00006 .00006 -3.7 00011 .00010 00010 .00010 00009 .00009 -3.6 00016 .00015 00015 .00014 00014 .00013 .00013 00012 00012 -3.5 .00023 .00022 .00022 .00021 00020 .00019 00019 00018 00017 00034 00032 .00031 00030 .00029 .00028 .00027 .00026 00025 00048 00047 00045 .00043 00042 .000-40 .00039 .00038 00036 -3.2 .00069 .00066 .00064 .00062 00060 .00058 .00056 .00054 00052 -3.1 .00097 .00094 .00090 .00087 00084 .00082 .00079 .00076 00074 -3.0 00135 .00131 00126 00122 00118 .00114 00111 00107 00104 -2.9 00187 .00181 .00175 .00169 .00164 .00159 .00154 .00149 00144 -2.8 00256 .00248 00240 00233 00226 00219 00212 00205 .00199 -2.7 .00347 00336 .00326 00317 00307 .00298 .00289 00280 00272 -2.6 00466 00453 00440 00427 00415 00402 00391 00379 00368 -2.5 00621 00604 00587 00570 00554 00539 .00-23 00508 00494 -2.4 .00820 .00798 .00776 .00755 .00734 .00714 .00695 .00676 00657 -2.3 01072 01044 01017 00990 00964 .00939 .00914 .00889 00866 01390 01355 01321 01287 01255 01222 01191 .01160 01130 -2.1 01786 01743 01700 01659 01618 01578 01539 01500 01463 -2.0 02275 02222 02169 02118 02068 02018 01970 01923 01876 -1.9 02872 02807 02743 02680 02619 .02559 02500 02442 02385 -1.8 03593 03515 03438 03362 03288 03216 03144 03074 03005 -1.7 04457 04363 04272 04182 04093 04006 03920 -1.6 05480 .05370 05262 05155 05050 04947 04846 -1.5 06681 06552 06426 06301 06178 06057 05938 -1.4 08076 07927 07780 .07636 07493 07353 07215 .06811 -1.3 09680 09510 09342 09176 09012 08851 08691 08534 08379 08226 -1.2 11507 11314 11123 .10935 .10749 .10565 .10383 .10204 .10027 .09853 -1.1 .13567 13350 .13136 12924 12714 12507 12302 .12100 11900 11702 -1.0 15866 15625 15386 15151 14917 .14686 14457 .14231 14007 13786 03836 03754 03673 04746 04648 04551 05821 05705 05592 07078 06944 Appendix -0.9 18406 -0.8 21186 .18141 20897 -0.7 24196 23885 .26435 -0.6 27425 27093 -0.5 30854 30503 -0.4 .30153 29806 34458 .34090 .33724 .33360 -0.3 37828 .37448 .37070 -0.2 41683 41294 40905 -0.1 46017 45620 45224 .44828 -0.0 50000 49601 49202 38209 42074 .17879 .17619 20611 20327 23576 23270 26763 .17106 .19766 22965 .22663 26109 25785 29460 29116 .32636 .17361 20045 32997 .36693 40517 44433 48803 48405 48006 .36317 40129 .44038 16853 .19489 .09 .00003 .00005 .00008 .00011 .00017 .00024 .00035 .00050 .00071 00100 .00139 .00193 00264 00357 .00480 .00639 00842 01101 .01426 01831 02330 02938 .16109 .16602 .16354 .19215 .18943 .18673 22363 .22065 21770 .21476 24510 25463 25143 24825 28774 28434 28096 27760 32276 31918 31561 .31207 35942 .35569 35197 .34827 39743 39358 38974 38591 42858 42465 43644 43251 47608 47210 46812 46414
STANDARD NORMAL DISTRIBUTION: Table Values Represent AREA to the LEFT of the Z score.
Z
.00
.01
.02
.09
0.0 50000
0.1 53983
0.2 57926
0.3
0.4
50399 50798
54380 54776
58317 58706
.61791 62172
65542 .65910
66276
0.5 .69146 .69497 69847
.73237
.76424
0.6
72575
75804
.72907
.76115
0.7
0.8
78814 .79103 79389
0.9
81594 .81859
83891
1.1
95449
96080 96164
96327
.96712
.96856 96926
.96995
97062
.96784
97441
97381
97500 97558 97615
97670
97932
97982
98030 98077 98124
98169
.03
.04
.05
.06
.07
.08
51197 51595 $1994 52392 52790 53188 53586
55172 55567 55962 56356 56749 57142 57535
59095 59483 59871 .60257 .60642 .61026 .61409
62552 .62930 .63307 .63683 .64058 .64431 .64803 .65173
.66640 .67003 .67364 .67724 68082 68439 .68793
.70194 .70540 .70884 .71226 .71566 .71904 .72240
.73565 .73891 74215 .74537 .74857 75175 .75490
.76730 .77035 77337 .77637 77935 .78230 .78524
.79673 .79955 80234 .80511
80785
81057 81327
.82121 .82381 .82639 .82894 .83147 .83398 .83646
1.0 84134 .84375 .84614 .84849 85083 .85314 .85543 .85769 85993 .86214
.86433 .86650 86864 .87076 .87286 .87493 .87698 .87900 .88100 88298
1.2 .88493 88686 88877 .89065 .89251 .89435 .89617 .89796 89973 .90147
1.3
90320 90490 90658 .90824 .90988 91149 .91309 91466 91621 91774
1.4 91924 92073 92220 92364 92507 92647 92785 92922 93056 93189
1.5 93319 93448 .93574 .93699 93822 .93943 94062 94179 94295 94408
1.6 94520 94630 94738 94845 94950 95053 95154 95254 95352
1.7 95543 95637 95728 95818 .95907 95994
.96246
1.8 96407 96485 96562 .96638
1.9 97128 97193 97257 97320
2.0 97725 97778 97831 97882
98257 98300 .98341
98382
98645 98679 .98713 .98745
98956 98983 .99010 .99036 .99061 .99086 99111 .99134
99202 99224 99245
.99266 99286 99305 99324 99343
99413 .99430
99446 99461 99477 99492
99560 99573 99585 .99598 99609 99621
99674 .99683 99693
99702 99711 99720
99760 99767 99774 99781 99788 99795
99819
99825 .99831 99836 99841 99846 99851 99856
3.0 .99865 99869 99874 .99878 99882 .99886 99889 99893
3.1 99903 .99906 99910 .99913 .99916 .99918 .99921 99924
3.2 99931
99934 99936 99938 99940
99942 .99944 99946
3.2 .99931 .99934 .99936 .99938 .99940 .99942 .99944
3.3 99952 99953 .99955 99957 99958 .99960 99961
3.4 .99966 99968 99969 .99970 .99971 .99972
99978 .99979 99980
.99985 .99986 .99986
.99990 .99990 99991
99993 .99994 .99994
99996 99996 99996
98574
2.1 98214
2.2 98610
98422 .98461 98500
.98537
98778 98809 98840 98870
98899
2.3 98928
99158
2.4 .99180
99361
2.5 99379
99506
.99520
2.6 .99534
99632
99643
.99396
.99547
99664
99752
2.7 99653
.99728
2.8 99744
99801
2.9 99813
99896
.99946
99962
99973 .99974
99981 .99981 .99982
.99937 .99988 .99988
.99987
.99991
99992 .99992 99992
.99994 99994 .99995 99995
.99996 99996 99996 99997
33
4925
3.5 .99977 .99978
.99985
.99990
3.6 .99984
3.7 .99989
3.8 99993
99993
3.9 .99995 99995
99926
99948
99736
99807
99861
.99900
99929
99950
.99948
.99950
.99964
99965
.99975
99976
99983 99983
99989
99992
99995
99997
Transcribed Image Text:STANDARD NORMAL DISTRIBUTION: Table Values Represent AREA to the LEFT of the Z score. Z .00 .01 .02 .09 0.0 50000 0.1 53983 0.2 57926 0.3 0.4 50399 50798 54380 54776 58317 58706 .61791 62172 65542 .65910 66276 0.5 .69146 .69497 69847 .73237 .76424 0.6 72575 75804 .72907 .76115 0.7 0.8 78814 .79103 79389 0.9 81594 .81859 83891 1.1 95449 96080 96164 96327 .96712 .96856 96926 .96995 97062 .96784 97441 97381 97500 97558 97615 97670 97932 97982 98030 98077 98124 98169 .03 .04 .05 .06 .07 .08 51197 51595 $1994 52392 52790 53188 53586 55172 55567 55962 56356 56749 57142 57535 59095 59483 59871 .60257 .60642 .61026 .61409 62552 .62930 .63307 .63683 .64058 .64431 .64803 .65173 .66640 .67003 .67364 .67724 68082 68439 .68793 .70194 .70540 .70884 .71226 .71566 .71904 .72240 .73565 .73891 74215 .74537 .74857 75175 .75490 .76730 .77035 77337 .77637 77935 .78230 .78524 .79673 .79955 80234 .80511 80785 81057 81327 .82121 .82381 .82639 .82894 .83147 .83398 .83646 1.0 84134 .84375 .84614 .84849 85083 .85314 .85543 .85769 85993 .86214 .86433 .86650 86864 .87076 .87286 .87493 .87698 .87900 .88100 88298 1.2 .88493 88686 88877 .89065 .89251 .89435 .89617 .89796 89973 .90147 1.3 90320 90490 90658 .90824 .90988 91149 .91309 91466 91621 91774 1.4 91924 92073 92220 92364 92507 92647 92785 92922 93056 93189 1.5 93319 93448 .93574 .93699 93822 .93943 94062 94179 94295 94408 1.6 94520 94630 94738 94845 94950 95053 95154 95254 95352 1.7 95543 95637 95728 95818 .95907 95994 .96246 1.8 96407 96485 96562 .96638 1.9 97128 97193 97257 97320 2.0 97725 97778 97831 97882 98257 98300 .98341 98382 98645 98679 .98713 .98745 98956 98983 .99010 .99036 .99061 .99086 99111 .99134 99202 99224 99245 .99266 99286 99305 99324 99343 99413 .99430 99446 99461 99477 99492 99560 99573 99585 .99598 99609 99621 99674 .99683 99693 99702 99711 99720 99760 99767 99774 99781 99788 99795 99819 99825 .99831 99836 99841 99846 99851 99856 3.0 .99865 99869 99874 .99878 99882 .99886 99889 99893 3.1 99903 .99906 99910 .99913 .99916 .99918 .99921 99924 3.2 99931 99934 99936 99938 99940 99942 .99944 99946 3.2 .99931 .99934 .99936 .99938 .99940 .99942 .99944 3.3 99952 99953 .99955 99957 99958 .99960 99961 3.4 .99966 99968 99969 .99970 .99971 .99972 99978 .99979 99980 .99985 .99986 .99986 .99990 .99990 99991 99993 .99994 .99994 99996 99996 99996 98574 2.1 98214 2.2 98610 98422 .98461 98500 .98537 98778 98809 98840 98870 98899 2.3 98928 99158 2.4 .99180 99361 2.5 99379 99506 .99520 2.6 .99534 99632 99643 .99396 .99547 99664 99752 2.7 99653 .99728 2.8 99744 99801 2.9 99813 99896 .99946 99962 99973 .99974 99981 .99981 .99982 .99937 .99988 .99988 .99987 .99991 99992 .99992 99992 .99994 99994 .99995 99995 .99996 99996 99996 99997 33 4925 3.5 .99977 .99978 .99985 .99990 3.6 .99984 3.7 .99989 3.8 99993 99993 3.9 .99995 99995 99926 99948 99736 99807 99861 .99900 99929 99950 .99948 .99950 .99964 99965 .99975 99976 99983 99983 99989 99992 99995 99997
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