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GATE 2016 ME (ME2) – Question 6

General Aptitude · Analytical Aptitude: Logical Reasoning and Deduction · 2 marks · Multiple choice

Students taking an exam are divided into two groups, P and Q such that each group has the same number of students. The performance of each of the students in a test was evaluated out of 200 marks. It was observed that the mean of group P was 105, while that of group Q was 85. The standard deviation of group P was 25, while that of group Q was 5. Assuming that the marks were distributed on a normal distribution, which of the following statements will have the highest probability of being TRUE?

  1. No student in group Q scored less marks than any student in group P.
  2. No student in group P scored less marks than any student in group Q.
  3. Most students of group Q scored marks in a narrower range than students in group P.
  4. The median of the marks of group P is 100.

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Show answer and explanation

Correct answer: (C) Most students of group Q scored marks in a narrower range than students in group P.

Explanation

Group Q has standard deviation5 versus25 for P, so a comparable central proportion occupies a much narrower score interval in Q. This supports **C**. Different means do not ensure complete separation of all scores, and a normal distribution with mean105 has median105 rather than100.