Q2. Suppose that 20 percent of the bottles produced in a certain plant are defective. A defective bottle will be noticed by an inspector and be removed from the filling line with a probability 0.7. If a bottle is not defective, the probability is 0.1 that the inspector will think that it is effective and remove it from the filling line. (a) What is the probability that a random selected bottle is defective and is removed from the filling line? (b) What is the probability that a bottle will be removed from the filling line? (e) If a customer buys a bottle that has not been removed from the filling line, what is the probability that it is defective? (d) Consider the event that a bottle is defective and the event that a bottle is removed by the inspector. Are they independent? Explain.
Q2. Suppose that 20 percent of the bottles produced in a certain plant are defective. A defective bottle will be noticed by an inspector and be removed from the filling line with a probability 0.7. If a bottle is not defective, the probability is 0.1 that the inspector will think that it is effective and remove it from the filling line. (a) What is the probability that a random selected bottle is defective and is removed from the filling line? (b) What is the probability that a bottle will be removed from the filling line? (e) If a customer buys a bottle that has not been removed from the filling line, what is the probability that it is defective? (d) Consider the event that a bottle is defective and the event that a bottle is removed by the inspector. Are they independent? Explain.
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
Related questions
Question
Transcribed Image Text:Q 2.
Suppose that 20 percent of the bottles produced in a certain plant are defective. A defective
bottle will be noticed by an inspector and be removed from the filling line with a probability 0.7. If a bottle
is not defective, the probability is 0.1 that the inspector will think that it is effective and remove it from the
filling line.
(a) What is the probability that a random selected bottle is defective and is removed from the filling line?
(b) What is the probability that a bottle will be removed from the filling line?
(c) If a customer buys a bottle that has not been removed from the filling line, what is the probability that
it is defective?
(d) Consider the event that a bottle is defective and the event that a bottle is removed by the inspector.
Are they independent? Explain.
Appendix
Z
.01
.02
.03
04
.07
STANDARD NORMAL DISTRIBUTION: Table Values Represent AREA to the LEFT of the Z score.
.00
-3.9 00005 .00005 00004 00004 00004
-3.8 00007 .00007
-3.7 00011 00010
-3.6 00016 .00015
-3.5 00023 00022
-3.4 00034 .00032
3.3
00048 .00047
-3.1 00097 .00094 .00090
00368 00357
.05 .06
.08
.09
.00004 00004 00004 .00003 .00003
00007 00006 00006
.00006 00006 00005 .00005 00005
00010 00010 00009 .00009 00008 00008 00008
00008
00015 00014 00014 .00013 00013 00012 00012 00011
00022 00021 00020 .00019 00019 00018 00017 00017
00031 00030 00029 .00028 00027 .00026 00025
00024
00045 00043 00042 .00040 .00039 .00038 .00036 .00035
00069 .00066 00064 00062 00060 .00058
00056 00054 00052
00050
00087 00084 00082 00079 00076 00074
00071
-3.0 00135 00131 00126 00122 00118 00114 00111 00107 00104 00100
00187 .00181 00175 .00169 00164 .00159 .00154 .00149 00144 00139
-2.8 00256 00248 00240 00233 00226 .00219 00212 00205 00199 .00193
-2.7 00347 00336 00326 00317 00307 00298 00289 00280 00272 00264
-2.6 00466 .00453 00440 00427 00415 .00402 00391 00379
-2.5 00621 00604 00587 00570 00554 00539
00820 00798 00776 00755 00734 00714
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 02938
-1.7 04457 04363 04272 04182 04093 04006 .03920 03836 03754 03673
-1.6 05480 05370 05262 05155
05050 04947 04846 04746 04648
04551
-1.5 06681 06552 06426 06301 06178 06057 05938 05821 05705 05592
-1.4 08076 07927 07780 07636 .07493 07353 07215 07078 06944 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
00423
00508
00494
00480
00695 00676 00657
00639
00842
01101
01426
-0.2
-0.1
01831
02330
-0.9 .18406 .18141 .17879 17619 .17361 .17106 .16853 .16602 .16354
-0.8 21186 20897 20611 20327 20045 .19766 .19489 .19215 .18943
-0.7 .24196 23885 23576
23270 22965 22663 22363
.22065 21770
27425 27093 26763 26435 26109 25785 25463
.30854 .30503 .30153 29806 29460 29116 28774 28434 28096
32997 .32636 32276 31918 31561 31207
35942 .35569 35197 34827
-0.6
25143 24825
-0.5
27760
-0.4
.34458 .34090
33724 33360
-0.3
.37448 37070
36693
.36317
.38209 37828
42074 41683
46017 45620
41294 40905
39743 39358 38974
38591
45224 44828
40517 40129
44433 44038
48006
42465
43644 43251 42858
47608 47210
46812
-0.0 50000 49601 49202 48803 48405
46414
.16109
.18673
21476
24510
Transcribed Image Text:STANDARD NORMAL DISTRIBUTION: Table Values Represent AREA to the LEFT of the Z. score.
Z
.00
.01
.07
.08
.09
0.0
53586
57535
.02
.03
50000 50399 50798 51197
0.1 53983 54380 54776 55172
0.2 57926 58317 58706 .59095
0.3 .61791 .62172 62552 .62930
66640
.61409
.65173
.68793
0.5
0.6
0.7
0.8
.72240
.75490
.78524
81327
83891
86214
88298
.90147
91774
93189
94408
95449
96327
97128 97193
97062
97670
.04
.05
.06
51595 51994 52392 52790 53188
55567 .55962 56356 56749 57142
59483 59871 60257 .60642 61026
.63307 .63683 64058 .64431 64803
0.4 .65542 65910 .66276
.67003 .67364 67724 .68082 68439
.69146 .69497 69847 .70194 .70540 .70884 71226 .71566 .71904
72575
72907 .73237 .73565 .73891 .74215 74537 .74857 75175
.75804 .76115 .76424 .76730 .77035 .77337 77637 77935 78230
78814 .79103 .79389 .79673 .79955 80234 80511 .80785 81057
0.9
.81594 81859
82121 .82381 .82639 82894 83147 .83398 83646
1.0 .84134 .84375 .84614 .84849 .85083 .85314 85543 .85769 85993
1.1 .86433 .86650 86864 .87076 .87286 .87493 .87698 .87900 88100
1.2 .88493 88686 .88877 .89065 .89251 .89435 .89617 .89796 89973
1.3
.90320 90490 .90658 90824 90988 .91149 91309 .91466 91621
1.4 91924 92073 92220 92364 92507 92647 92785 92922 93056
1.5 93319 93448
93574 93699 .93822 .93943 94062 .94179 94295
1.6 94520 94630 94738 94845 94950 .95053 95154 95254 95352
1.7 .95543 95637 95728 95818 95907 .95994 96080 .96164 96246
1.8 96407 96485
96562 96638 .96712 .96784 96856 .96926 96995
1.9
97257 97320 97381 97441 97500 97558 97615
2.0 97725 97778 97831 97882 97932 .97982 98030 98077 98124 98169
2.1 98214 98257 98300 .98341 98382 .98422 98461 98500 98537 98574
2.2 98610 98645 98679 98713 98745 98778 98809 98840 98870 98899
2.3 98928 98956
98983
99010 99036 .99061 99086 99111 99134 .99158
2.4 99180 99202 99224 99245 99266 99286 99305
99324 99343 99361
2.5 99379 .99396 99413 99430 99446 .99461 99477 99492 99506 99520
2.6 99534 .99547 99560 .99573 .99585 .99598 99609 .99621 99632
2.7 .99653 99664 99674 .99683 99693 99702
99711 .99720 99728
2.8 .99744 99752 99760 99767 .99774 99781 99788 99795 99801
2.9
99813 99819 99825 99831 99836 .99841 99846 99851 99856
3.0 .99865 99869 99874 99878 99882 99886 99889 99893 99896
3.1 99903 .99906 99910 99913 .99916 .99918
99921 99924 99926
99931 99934 99936 99938 99940 .99942 99944 99946 99948
3.2 .99931 .99934 .99936 .99938 99940 .99942 99944 .99946
3.3 99952 99953 .99955 99957 99958 99960 99961
3.4 .99966 99968 99969 .99970 99971 99972 99973
3.5 .99977 99978 99978 .99979 99980 .99981 99981
3.6 .99984 99985 .99985 .99986 99986 .99987 99937
3.7 99989 99990 .99990 99990 99991 .99991 99992
3.8 .99993 99993 99993 99994 99994 .99994 99994
3.9 99995 99995 .99996 .99996 99996 .99996 .99996
99643
99736
99807
99861
99900
99929
99950
.99948
.99962 99964
99974 .99975
.99982 99983
.99988 99988
99992 99992
.99995 .99995
99996 99997
.99950
99965
99976
99983
99989
.99992
99995
99997
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