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GATE2016-GA-6

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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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