Final answer:
Chebyshev's Theorem guarantees that at least 75% of quiz scores are between 5.5 and 7.5, representing scores within 1 standard deviation from the mean of 6.5.
Step-by-step explanation:
Using Chebyshev's Theorem to determine the minimum percentage of scores that fall within a specific range, we first find the number of standard deviations the range is from the mean. The range here is from 5.5 to 7.5, which is 1 standard deviation below and above the mean of 6.5 since the given standard deviation is 0.5. Chebyshev's Theorem states that at least (1 - 1/k^2) of the data lies within k standard deviations from the mean, for any k > 1.
Plugging k = 2 into Chebyshev's inequality (since 1 standard deviation is half of 2), we get at least (1 - 1/4), or 75%, of the scores between 5.5 and 7.5. This is the minimum percentage guaranteed by the theorem, regardless of the actual distribution of the scores.