Answer:
Assuming that the distribution of section scores is still approximately normal with a mean of 500 and a standard deviation of 100, we can use the empirical rule (also known as the 68-95-99.7 rule) to estimate the probability that a randomly-selected student gets a section score of 700 or better.
According to the empirical rule, approximately 68% of the scores fall within one standard deviation of the mean, approximately 95% of the scores fall within two standard deviations of the mean, and approximately 99.7% of the scores fall within three standard deviations of the mean.
To estimate the probability of getting a section score of 700 or better, we need to find the proportion of scores that are more than two standard deviations above the mean.
Z-score = (X - μ) / σ = (700 - 500) / 100 = 2
From the standard normal distribution table, we find that the proportion of scores that are more than 2 standard deviations above the mean is approximately 0.0228.
Therefore, the estimated probability that a randomly-selected student gets a section score of 700 or better is about 0.0228, or 2.28%.
Explanation: