In each of the following independent problems, design a systematic sampling plan with one start. The plan should include defining the sampling unit, establishing a numbering system for the population, and establishing a correspondence between the random number table and the population in order to arrive at a starting point. The sample should be designed to select 50 items from the population. After the plan has been designed, select the first five sample items for each problem. As a starting point, use Figure 2-1, item 1003, column 2, for each problem. If that number results in a discard, read down the table to arrive at a starting point, using the left-most digits in the column,

a. Prenumbered sales invoices in a sales journal, where the lowest invoice number is 1 and the highest is 6211.

b. Prenumbered bills of lading, where the lowest document number is 21926 and the highest is 28511.

c. Accounts receivable, on ten pages with 60 lines per page. Each line has a customer name and an amount receivable, except the last page, which has only 36 full lines.

d. Prenumbered invoices in a sales journal, where each month starts over with number 1. (Invoices for each month are designated by the month and document number.) There are a maximum of 20 pages per month, with a total of 185 pages for the year. All pages have 75 invoices, except for the last page of each month.

Figure 2-1:

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Columns Item (1) (2) (3) (4) (6) (7) 1000 37039 97547 64673 31546 99314 66854 97855 99965 1001 25145 84834 23009 51584 66754 77785 52357 25532 1002 98433 54725 18864 65866 76918 78825 58210 76835. 1003 97965 68548 81545 82933 93545 85959 63282 61454 1004 78049 67830 14624 17563 25697 07734 48243 94318 1005 50203 25658 91478 08509 23308 48130 65047 77873 1006 40059 67825 18934 64998 49807 71126 77818 56893 1007 84350 67241 54031 34535 04093 35062 58163 14205 1008 30954 51637 91500 48722 60988 60029 60873 37423 1009 86723 364641 98305 08009 00666 29255 18514 49158 1010 50188 22554 86160 92250 14021 65859 16237 72296 1011 50014 00463 13906 35936 71761 95755 87002 71667 1012 66023 21428 14742 94874 23308 58533 26507 11208 1013 04458 61862 63119 09541 01715 87901 91260 03079 1014 57510 36314 30452 09712 37714 95482 30507 68475 1015 43373 58939 95848 28288 60341 52174 11879 18115 1016 61500 12763 64433 02268 57905 72347 49498 21871 1017 78938 71312 99705 71546 42274 23915 38405 18779 1018 64257 93218 35793 43671 64055 88729 11168 60260 1019 56864 21554 70445 24841 04779 56774 96129 73594 1020 35314 29631 06937 54545 04470 75463 77112 77126 1021 40704 48823 65963 39359 12717 56201 22811 24863 1022 07318 44623 02843 33299 59872 86774 06926 12672 1023. 94550 23299 45557 07923 75126 00808 01312 46689 1024 34348 81191 21027 77087 10909 03676 97723 34469 1025 92277 57115 50789 68111 75305 53289 39751 45760 1026 56093 58302 52236 64756 50273 61566 61962 93280 1027 16623 17849 96701 94971 94758 08845 32260 59823 1028 50848 93982 66451 32143 05441 10399 17775 74169 1029 48006 58200 58367 66577 68583 21108 41361 20732 1030 56640 27890 28825 96509 21363 53657 60119 75385 FIGURE 2-1 Random number table