GATE 2021 MT – Question 25
Annealed-specimen grain size $X$ has a symmetric distribution with mean $\mu=5$ μm and standard deviation $\sigma=0.5$ μm. Given $P(X\le\mu+2\sigma)=0.98$, the percentage with grain size 5–6 μm is ______ % (nearest integer).
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Correct answer: 48 to 48
Explanation
The supplied symmetric distribution has P(X≤μ+2σ)=0.98 and P(X≤μ)=0.50. Their difference is 0.48. Since 6 μm=μ+2σ, the requested percentage is **48%**; no normal-distribution assumption is necessary.