In which subject did Aman do better compared…

In which subject did Aman do better compared with the other candidates?

Question 22

MediumOriginal question

In a board's Mathematics exam the marks are normal with mean 60 and standard deviation 8; in its English exam they are normal with mean 55 and standard deviation 10. Aman scores 76 in Mathematics and 70 in English. (Take $P(0 < Z < 1) = 0.3413$ .)

In which subject did Aman do better compared with the other candidates?

English: he is 15 marks above the mean there, against 16 in MathematicsCorrect answerYour answerMathematics: his

z

-score is 2, against 1.5 in EnglishCorrect answerYour answerMathematics, because 76 is more than 70Correct answerYour answerEqually well in bothCorrect answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer B

Correct answer: B

Mathematics: $z = \frac{76 - 60}{8} = 2$ . English: $z = \frac{70 - 55}{10} = 1.5$ .
A higher $z$ -score means a better standing, so Mathematics.

Worth noting

Raw marks cannot be compared across exams with different means and spreads.

Concept: Comparing scores through z
Typical timeTypical: 120 s
Your timeYours: —

The rule this testsThe standard normal variate

Practise this chapter →

Ten questions from Normal Distribution, at your own pace.

Practise this chapter →

Ten questions from Normal Distribution, at your own pace.

In which subject did Aman do better compared with the other candidates?

Question 22

Explanation