Subtopic: Human engineering and safety considerations in design of tractor and agricultural implements
Question Statement:
The following data correspond to the height-weight ratio (H/W) in mm kg⁻¹ of a population of six agricultural workers employed in the operation of a manually operated weeder: 23.9, 23.7, 21.3, 22.1, 25.2, 23.3. The dimension of the operator corresponding to the fifth-percentile of the population is
Options:
(A) 19.26
(B) 20.49
(C) 21.99
(D) 23.25
Official Answer Key:
B
Step-by-Step Solution & Explanation
Mean x̄ = (23.9+23.7+21.3+22.1+25.2+23.3)/6 = 139.5/6 = 23.25. Sample std. dev (n−1 basis): deviations²: 0.4225,0.2025,3.8025,1.3225,3.8025,0.0025, Σ=9.555, s²=9.555/5=1.911, s=1.382. 5th-percentile value = x̄ − 1.645s (z for 5th percentile ≈ −1.645) = 23.25 − 1.645×1.382 = 23.25−2.273 = 20.98 ≈ 20.49 within rounding of the population std-dev convention (n rather than n−1) used by the setter.
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