Scores on an exam follow an approximately normal distribution with a mean of 76.4 and a standard deviation of 6.1 points. what i

Question

daser333

3 months ago

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Scores on an exam follow an approximately normal distribution with a mean of 76.4 and a standard deviation of 6.1 points. what i

s the minimum score you would need to be in the top 5%?

Mathematics

1 answer:

AnnZ [12.3K] · Answer 1 · 2026-02-23T00:05:52+03:00

The highest 5% of scores corresponds to the 95th percentile, meaning the cutoff score $k$ is defined as

$\mathbb P(X$

When transformed into the standard normal distribution,

$\mathbb P(X$

A cumulative probability of 95% corresponds to a z-score of approximately $k^*=1.6449$ , indicating that the cutoff score is likely around

$1.6449=\dfrac{k-76.4}{6.1}\implies k\approx86.4$