0 votes

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 $\text{TRUE}$?

- No student in group $Q$ scored less marks than any student in group $P.$
- No student in group $P$ scored less marks than any student in group $Q.$
- Most students of group $Q$ scored marks in a narrower range than students in group $P.$
- The median of the marks of group $P$ is $100$.