Assuming scores are normally distributed, a score of 82% on Ms. Smith's test corresponds to the
-th percentile, i.e.

where
is a random variable denoting scores on Ms. Smith's test.
Transform
to
, which follows the standard normal distribution:

which means Amy scored at the 99.98th percentile.
This makes it so that Karina needs to score
on Mr. Adams' test so that

Their test scores have the same
score computed above, so

so Karina needs to get a test score of at least 83.5%.