Answer:
At most 12.5% of the scores are above 92.
Step-by-step explanation:
Chebyshev's theorem states that:
At least 75% of the measures are within 2 standard deviations of the mean.
At least 89% of the measures are within 3 standard deviations of the mean.
In this problem, we have that:
Mean = 81%
Standard deviation = 5.5%
Using Chebyshev's Theorem what can we say about the percentage of scores that are above 92?
92 = 81 + 2*5.5
So 92 is two standard deviations above the mean.
By the Chebyshev's theorem, at least 75% of the measures are within 2 standard deviations of the mean. So at most 25% is more than 2 standard deviations from the mean. Chebyshev's theorem works with symmetric distributions, so, of those at most 25%, at most 12.5% are more than 2 standard deviations below the mean and at most 12.5% are more than 2 standard deviations above the mean.
So at most 12.5% of the scores are above 92.
