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GATE 2019 ME (ME1) – Question 14

Engineering Mathematics · Probability and Statistics: Mean, median, mode, standard deviation, random variables and distributions · 1 mark · Multiple choice

Titanium rod lengths are normally distributed with mean 440 mm and standard deviation 1 mm. What percentage lies between 438 mm and 441 mm?

  1. 81.85%
  2. 68.4%
  3. 99.75%
  4. 86.64%

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Correct answer: (A) 81.85%

Explanation

Standardize with $Z=(L-440)/1$. The bounds become $-2$ and $1$. Therefore the probability is $\Phi(1)-\Phi(-2)=0.84134-0.02275=0.81859$, or **81.85%, A**.