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Tech. students is composed of four batches A, B, C and D, each consisting of 30 students. It is found that the sessional marks of students in Engineering Drawing in batch Chave a mean of 6.6 and standard deviation of 2.3. The mean and standard deviation of the marks for the entire class are 5.5 and 4.2, respectively. It is decided by the course instructor to normalize the marks of the students of all batches to have the same mean and standard deviation as that of the entire class. Due to this, the marks of a student in batch C are changed from 8.5 to A. 6.0 B. 7.0
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Answer is Wrong!
Answer is Right!
The correct answer is $\boxed{\text{B}}$.
To normalize the marks, we subtract the mean of the batch from each mark and then divide by the standard deviation of the batch. In this case, the mark of the student in batch C is changed from $8.5$ to $\frac{8.5 – 6.6}{2.3} = 7.0$.
Here is a brief explanation of each option:
- Option A: $6.0$. This is the mean of the marks for the entire class. However, the student in batch C already has a mark that is above the mean, so it would not make sense to reduce their mark to the mean.
- Option B: $7.0$. This is the mark that the student in batch C would have if their mark were normalized. This is the correct answer.
- Option C: $8.0$. This is the mark that the student in batch C would have if their mark were not normalized. However, the instructor has decided to normalize the marks, so this is not the correct answer.
- Option D: $9.0$. This is a mark that is above the mean of the marks for the entire class. However, the student in batch C already has a mark that is above the mean, so it would not make sense to increase their mark even further.