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GATE 2024 MT – Question 13

Engineering Mathematics · Probability and statistics · 1 mark · Multiple choice

The figure shows normal distributions $a,b,c$. For distribution $p$, $\sigma_p$ is standard deviation and $\mu_p$ is mean; all means are positive. Which deduction is correct?

Diagram for GATE 2024 MT question 13
  1. $\sigma_a<\sigma_b<\sigma_c$
  2. $\sigma_a>\sigma_b>\sigma_c$
  3. $\mu_a=\mu_b=\mu_c$
  4. $\mu_a>\mu_b>\mu_c$

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Correct answer: (A) $\sigma_a<\sigma_b<\sigma_c$

Explanation

For a normal density, the peak height is inversely proportional to σ and the horizontal spread increases with σ.

Curve a is tallest/narrowest, b intermediate, and c lowest/broadest.

Hence **σa<σb<σc, A**.

Their displaced centres do not imply equal means.