GATE 2025 PI – Question 19
Industrial Engineering · Work System Design · 1 mark · Multiple choice
A worker is idle in x of n work-sampling observations. Find the standard deviation of estimated mean idle proportion.
- $\sqrt{x^2/n^3}$
- $\sqrt{x(n-x)/n^3}$
- $\sqrt{x(n-x)/n^2}$
- $x/n$
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Show answer and explanation
Correct answer: (B) $\sqrt{x(n-x)/n^3}$
Explanation
Estimated idle probability is $\hat p=x/n$. The estimated standard error is $\sqrt{\hat p(1-\hat p)/n}=\sqrt{x(n-x)/n^3}$. Thus **B**.
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