What mark would Johnny have had to score in Mathematics for his performance to be equivalent to that for English?

Question

Johnny scored 55 in an English test for which the mean score was 50 and the standard

deviation was 6. He scored 64 in a Mathematics test for which the mean score was 59

and the standard deviation 9. If the scores have a normal distribution, in which subject

did he perform better? What mark would Johnny have had to score in Mathematics for

his performance to be equivalent to that for English?

Answer 1

In this case we need to calculate P(Z < 55 - 50 / 6) and P(Z < 64 - 59 / 9)

P(Z < 5/6) and P(Z<5/9)

Since 5/6 is greater than 5/9, P(Z < 5/6) > P(Z< 5/9) so he performed better, statistically speaking, on the English test.

In order to figure out how high his score needs to be (call this t) to do as well, statistically speaking, we just need to solve the equation (t - 59)/ 9 = 5/6, since P(Z< t - 59/6) has to be equal to P(Z< 5/6).

t - 59 = 45/6

t = 59 + 45/6 = 59 + 7.5 = 66.5 percent