A student scored 70 marks in Mathematics, where the marks of the class have mean 60 and standard deviation 8, and 80 marks in English, where the marks of the class have mean 72 and standard deviation 5. Comparing with the class, the subject in which the student did better and the value of the standard normal variate of his marks in that subject are
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → English, 1.6
Marks on different scales are compared through the standard normal variate \(Z = \frac{X - \mu}{\sigma}\), which tells how many standard deviations a score lies above the mean.
Mathematics:
\( \displaystyle Z = \frac{70 - 60}{8} = 1.25 \)
English:
\( \displaystyle Z = \frac{80 - 72}{5} = 1.6 \)
Since 1.6 > 1.25, the student did better in English compared with the class, with Z = 1.6.
Why the other options are incorrect
Option (1) Mathematics, 1.25 — Incorrect. 1.25 is the Mathematics value, but it is smaller than the English value 1.6.
Option (2) Mathematics, 10 — Incorrect. 10 is only the raw gap 70 − 60; it has not been divided by the standard deviation 8.
Option (4) English, 8 — Incorrect. 8 is only the raw gap 80 − 72; it has not been divided by the standard deviation 5.