Question

the ceo of a company wants to determine if taking the employees to a company retreat would boost their morale. he decides to use a random number table to survey a simple random sample of 50 of the 250 employees. the employees are assigned the numbers 001 - 250. refer to the given line from a random number table. which numbers represent the first 3 members selected? 46254 58160 09695 38399 40400 32662 462, 545, 816 009, 040, 032 160, 096, 040 046, 025, 045

Explanation:

Step1: Analyze each option

• Option1: 462, 545, 816 are all greater than 250, so they are not valid.
• Option2: 009 (9), 040 (40), 032 (32) are all within 1 - 250.
• Option3: 096 (96) is valid, but 160 is from the original number 58160 (if we take 3 - digit numbers, 581 is invalid as it's > 250, 160 is from 58160 but the way of extraction is not correct as per 3 - digit grouping starting from left), 040 (40) is valid. But the extraction method for 160 is wrong.
• Option4: 046 (46) is valid, 025 (25) is valid, 045 (45) is valid. But let's check the random - number - table reading. We read the random number table in groups of 3 digits. Starting from the left: 462 (invalid as > 250), 545 (invalid as > 250), 816 (invalid as > 250), 096 (96, valid), 953 (invalid as > 250), 839 (invalid as > 250), 940 (invalid as > 250), 400 (invalid as > 250), 326 (invalid as > 250), 62... If we consider the correct 3 - digit reading without skipping (in a proper way of simple random sampling using the table), when we start from the leftmost 3 - digit number:
• The first 3 - digit number is 462 (>250, skip).
• The second 3 - digit number is 545 (>250, skip).
• The third 3 - digit number is 816 (>250, skip).
• The fourth 3 - digit number is 096 (96, valid).
• The fifth 3 - digit number is 953 (>250, skip).
• The sixth 3 - digit number is 839 (>250, skip).
• The seventh 3 - digit number is 940 (>250, skip).
• The eighth 3 - digit number is 400 (>250, skip).
• The ninth 3 - digit number is 326 (>250, skip).
• The tenth 3 - digit number is 662 (>250, skip). But if we consider the standard way of reading from left to right, 3 - digit by 3 - digit:
• The first valid 3 - digit number (≤250) is 096 (96). But if we consider the options given, for option2:
• If we assume that we can re - group (in some cases, when starting a new group after an invalid number), 009 (9), 040 (40), 032 (32) are valid. When we read the random number table as 462 (invalid), 54 (invalid, but if we consider 3 - digit numbers starting from the next digit after 462: 581 (invalid), 600 (invalid), 969 (invalid), 538 (invalid), 399 (invalid), 404 (invalid), 003 (3, written as 003), 266 (invalid). But if we consider another approach of taking non - overlapping 3 - digit numbers from the left:
• The first 3 - digit number: 462 (invalid).
• The second 3 - digit number: 581 (invalid).
• The third 3 - digit number: 600 (invalid).
• The fourth 3 - digit number: 969 (invalid).
• The fifth 3 - digit number: 538 (invalid).
• The sixth 3 - digit number: 399 (invalid).
• The seventh 3 - digit number: 404 (invalid).
• The eighth 3 - digit number: 003 (3, written as 003). But if we consider the options, option2 has numbers 009 (9), 040 (40), 032 (32) which can be obtained by proper 3 - digit grouping (e.g., 09695383994040032662: group as 096 (invalid as 96 is valid but not in the option), 953 (invalid), 839 (invalid), 940 (invalid), 400 (invalid), 326 (invalid). But if we consider the number 462545816009695383994040032662 and group as 009 (from 462545816009...), 040 (from... 096953839940...), 032 (from... 4040032662).

Answer:

009, 040, 032