A preliminary survey indicates that 20% of the time of a gang of workers is spent ideally. What is the total number of observations required to determine the proportion of idle time within ±5% with 95% confidence limit ?
- A216 observations
- B226 observations
- C246 observationsCorrect
- D236 observations
Solution
Concept
Number of observations in work sampling
Formula
N = z² p (1 − p) / E²
Step-by-step solution
1. p = 0.20, E = 0.05, z = 1.96. 2. N = 1.96² × 0.20 × 0.80 / 0.05² = 3.8416 × 0.16 / 0.0025 = 245.9 ≈ 246.
Explanation
Work sampling uses the binomial approximation; the sample size depends on the proportion, the allowed absolute error and the confidence level.
Why the other options are wrong
216, 226 and 236 are below the 246 needed.
Shortcut
N = z² p q / E².
Common mistake
Using z = 2 gives 256, which is not an option.
Correct answer: C) 246 observations