Project ForgeStudents 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?
- ANo student in group Q scored less marks than any student in group P.
- BNo 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.
- DThe median of the marks of group P is 100.
Explanation
Group Q's standard deviation (5) is much smaller than group P's (25), meaning Q's scores cluster tightly around its mean while P's scores are spread widely. This makes it highly likely that most of group Q's students scored within a narrow range compared to group P's much wider spread. The absolute 'no student' claims (A, B) are far too strong given normal distributions have overlapping tails, and nothing establishes the median of P is exactly 100 (for a normal distribution, median = mean = 105).
Source: GATE ME 2016 Set-2 (2016)
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