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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%.