(e) Referring to Part (b), what is the probability that a sample mean will be outside 5±30, just by chance (that is, when there are no unusual circumstances)? (d) Suppose that a machine used to apply the coating is out of adjustment, resulting in a mean coating thickness of 4.95mm. What is the probability that a problem will be detected when the next sample is taken?

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6th Edition
ISBN:9781119256830
Author:Amos Gilat
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Q 5.
The thickness (in millimeters) of the coating applied to disk drives is one characteristic that
determines the usefulness of the product. When no unusual circumstances are present, the thickness (z) has
a normal distribution with a mean of 5mm and a standard deviation of 0.1mm. Suppose that the process
will be monitored by selecting a random sample of 30 drives from each shift's production and determining 2,
the mean coating thickness for the sample. (Round your answer to 4 decimal places if any.)
(b) When no unusual circumstances are present, we expect 2 to be within 30, of 5mm, the desired value.
An z value farther from 5 than 30, is interpreted as an indication of a problem that needs attention.
Compute 5+ 30,
(c) Referring to Part (b), what is the probability that a sample mean will be outside 5+30, just by chance
(that is, when there are no unusual circumstances)?
(d) Suppose that a machine used to apply the coating is out of adjustment, resulting in a mean coating
thickness of 4.95mm. What is the probability that a problem will be detected when the next sample is
taken?
Q(b) is not needed and it is given as a reference jusst solve for Qc) and Qd).i
will be very appreciate!!
-0.4
-0.3
Appendix
STANDARD NORMAL DISTRIBUTION: Table Values Represent AREA to the LEFT of the Z. score.
J02
Z
.00
.01
.05
-3.9
00005 00005 00004 00004
00004
.06 007
.09
00004 00004 00003 .00003
.00005
.00008
-3.8
00007 00007 00007
00006
00006 .00005 00005
00009
00008
00008 00008
00011 00010 00010 00010
00016 00015 00015 00014
00023 00022 00022 00021
00034 00032 00031 00030
00048 00047 00045 00043
00069 00066 00064 00062
00058 00056 00054 00052
-3.1 00097 00094 00090 .00087
00082 00079 00076 00074
-3.0 00135 00131 00126 00122
00118 00114 00111 00107 00104
00187 00181 00175 .00169 00164 00159 00154 .00149 00144
00256 00248 00240 .00233 .00226 00219 00212 00205 .00199
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
00820 00798 00776 00755
00695 00676 00657
01072 01044 01017 00990 00964
01390 01355 01321
01255
01786
01618
-2.0 02275 02222 02169 02118 02068
-1.9 02872 02807 02743 02680 02619
-1.8 03593 03515 03438 03362 03288
-1.7 04457 04363 04272 04182 04093
01287
01743 01700 01659
00734 00714
00939 00914 00889 00866
01222 01191 01160 01130
01578 01539 01500 01463
02018 01970 01923 01876
02385
03074 03005
03836 03754
01831
02330
02938
04746 04648
05821 05705
02559 02500
03216 03144
04006 03920
03673
-1.6 05480 05370 05262 05155 05050 04947 04846
04551
-1.5 06681 06552 06426 06301 06178 06057 05918
05592
-1.4 08076 07927 07780 07636 07493 07353 07215 07078 06944 06811
09680 09510 09342 09176 09012 08851 08691 08534 08379 08226
11507 11314 11123 10935 10749 -10565 .10383 .10204 10027 09853
13567 13350 13136 12924 12714 12507 12302 12100
11900
11702
15866 15625 .15386 15151 -14917 -14686 14457 14231 14007 13786
-0.2
-0.1
-0.0
-2.3
-0.9 .18406 .18141
-0.8 21186 20897 20611
-0.7 .24196
23885
-0.6 27425
27093
-0.5 30854 30503 30153
-1.2
-1.1
.17879 .17619
20327
23576
26763
34458 .34090 33724
38209 37828 37448
42074 41683 41294
46017 45620 45224
50000 49601 49202
.04
00004
00006
00009
00014
00013
00020 00019
.00029 .00028
00042
00060
00084
17361
20045
00013
00012 00012
00019 00018 00017
00027 00026 00025
00040 00039 00038 00036
02442
.00011
00017
.00024
.00035
.00050
.00071
00100
.00139
.00193
00264
.00357
.00480
.00639
00842
17106 .16853
.16109
.19766 .19489
18673
23270
22965
.22663 22363
21476
26435
26109
24510
29806 29460
27760
31207
25785 25463
29116
.32636 32276 31918
.36317
40129
.44038
48803 48405 48006 47608
35942 .35569
35197
33360 32997
37070 36693
40905 40517
44828 44433
34827
39743 .39358 38974
38591
43644 43251 42858 42465
47210 46812 46414
01101
01426
.16602 .16354
19215 .18943
22065 21770
24825
25143
28774 28434 28096
31561
Transcribed Image Text:Q 5. The thickness (in millimeters) of the coating applied to disk drives is one characteristic that determines the usefulness of the product. When no unusual circumstances are present, the thickness (z) has a normal distribution with a mean of 5mm and a standard deviation of 0.1mm. Suppose that the process will be monitored by selecting a random sample of 30 drives from each shift's production and determining 2, the mean coating thickness for the sample. (Round your answer to 4 decimal places if any.) (b) When no unusual circumstances are present, we expect 2 to be within 30, of 5mm, the desired value. An z value farther from 5 than 30, is interpreted as an indication of a problem that needs attention. Compute 5+ 30, (c) Referring to Part (b), what is the probability that a sample mean will be outside 5+30, just by chance (that is, when there are no unusual circumstances)? (d) Suppose that a machine used to apply the coating is out of adjustment, resulting in a mean coating thickness of 4.95mm. What is the probability that a problem will be detected when the next sample is taken? Q(b) is not needed and it is given as a reference jusst solve for Qc) and Qd).i will be very appreciate!! -0.4 -0.3 Appendix STANDARD NORMAL DISTRIBUTION: Table Values Represent AREA to the LEFT of the Z. score. J02 Z .00 .01 .05 -3.9 00005 00005 00004 00004 00004 .06 007 .09 00004 00004 00003 .00003 .00005 .00008 -3.8 00007 00007 00007 00006 00006 .00005 00005 00009 00008 00008 00008 00011 00010 00010 00010 00016 00015 00015 00014 00023 00022 00022 00021 00034 00032 00031 00030 00048 00047 00045 00043 00069 00066 00064 00062 00058 00056 00054 00052 -3.1 00097 00094 00090 .00087 00082 00079 00076 00074 -3.0 00135 00131 00126 00122 00118 00114 00111 00107 00104 00187 00181 00175 .00169 00164 00159 00154 .00149 00144 00256 00248 00240 .00233 .00226 00219 00212 00205 .00199 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 00820 00798 00776 00755 00695 00676 00657 01072 01044 01017 00990 00964 01390 01355 01321 01255 01786 01618 -2.0 02275 02222 02169 02118 02068 -1.9 02872 02807 02743 02680 02619 -1.8 03593 03515 03438 03362 03288 -1.7 04457 04363 04272 04182 04093 01287 01743 01700 01659 00734 00714 00939 00914 00889 00866 01222 01191 01160 01130 01578 01539 01500 01463 02018 01970 01923 01876 02385 03074 03005 03836 03754 01831 02330 02938 04746 04648 05821 05705 02559 02500 03216 03144 04006 03920 03673 -1.6 05480 05370 05262 05155 05050 04947 04846 04551 -1.5 06681 06552 06426 06301 06178 06057 05918 05592 -1.4 08076 07927 07780 07636 07493 07353 07215 07078 06944 06811 09680 09510 09342 09176 09012 08851 08691 08534 08379 08226 11507 11314 11123 10935 10749 -10565 .10383 .10204 10027 09853 13567 13350 13136 12924 12714 12507 12302 12100 11900 11702 15866 15625 .15386 15151 -14917 -14686 14457 14231 14007 13786 -0.2 -0.1 -0.0 -2.3 -0.9 .18406 .18141 -0.8 21186 20897 20611 -0.7 .24196 23885 -0.6 27425 27093 -0.5 30854 30503 30153 -1.2 -1.1 .17879 .17619 20327 23576 26763 34458 .34090 33724 38209 37828 37448 42074 41683 41294 46017 45620 45224 50000 49601 49202 .04 00004 00006 00009 00014 00013 00020 00019 .00029 .00028 00042 00060 00084 17361 20045 00013 00012 00012 00019 00018 00017 00027 00026 00025 00040 00039 00038 00036 02442 .00011 00017 .00024 .00035 .00050 .00071 00100 .00139 .00193 00264 .00357 .00480 .00639 00842 17106 .16853 .16109 .19766 .19489 18673 23270 22965 .22663 22363 21476 26435 26109 24510 29806 29460 27760 31207 25785 25463 29116 .32636 32276 31918 .36317 40129 .44038 48803 48405 48006 47608 35942 .35569 35197 33360 32997 37070 36693 40905 40517 44828 44433 34827 39743 .39358 38974 38591 43644 43251 42858 42465 47210 46812 46414 01101 01426 .16602 .16354 19215 .18943 22065 21770 24825 25143 28774 28434 28096 31561
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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