The 840 workers of a factory are numbered 1 to 840. A systematic random sample of 35 workers is drawn, and the first worker selected is worker number 17. Which of the following workers is NOT in the sample?
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → Worker number 563
The sampling interval is
\( \displaystyle k = \frac{840}{35} = 24 \)
So the sample consists of workers 17, 41, 65, …, that is, the numbers of the form \(17 + 24m\) (m = 0, 1, 2, …, 34).
A worker is in the sample exactly when (number − 17) is a multiple of 24.
For worker 563, \(563 - 17 = 546 = 24 \times 22 + 18\), which is not a multiple of 24. So worker 563 is not in the sample.
Why the other options are incorrect
Option (1) Worker number 185 — Incorrect. \(185 - 17 = 168 = 24 \times 7\), so this worker is in the sample.
Option (2) Worker number 401 — Incorrect. \(401 - 17 = 384 = 24 \times 16\), so this worker is in the sample.
Option (3) Worker number 521 — Incorrect. \(521 - 17 = 504 = 24 \times 21\), so this worker is in the sample.