In which test did A actually perform best relative to other students?
To find out we have to calculate the performance of student in comparison to other students appearing in the same test
In Test 1,
$\mu _1$ = 74 , $\sigma_1 = 11$
$Z_1 = \frac{X_1 - \mu_1}{\sigma_1} = \frac{80 - 74}{11} = 0.545 $
Area to the left of Z is 0.705402 so the student performed better than $70.54 \%$ students in test1.
$\mu _2$ = 75 , $\sigma_2 = 10$
$Z_2 = \frac{X_2 - \mu_2}{\sigma_2} = \frac{81 - 75}{10} = 0.6$
Area to the left of Z is 0.725747 so the student performed better than $72.57 \%$ students in test2.
$\mu _3$ = 78 , $\sigma_3 = 14$
$Z_3 = \frac{X_3 - \mu_3}{\sigma_3} = \frac{86 - 78}{14} = 0.571$
Area to the left of Z is 0.715661 so the student performed better than $71.56 \%$ students in test3.
$\mu _4$ = 82 , $\sigma_4 = 13$
$Z_4 = \frac{X_4 - \mu_4}{\sigma_4} = \frac{89 - 82}{13} = 0.538$
Area to the left of Z is 0.701944 so the student performed better than $70.19 \%$ students in test4.
So from this we can conclude that student performed better in 2nd Test relative to other students.