Final answer:
Using the Empirical Rule, the proportion of sixth-grade students who read less than 77 words per minute is 2.5%, and those who read more than 149 words per minute make up 16%.
Step-by-step explanation:
To answer parts (f) and (g) of the question using the Empirical Rule (which states that for a normal distribution, approximately 68% of the data falls within one standard deviation of the mean, 95% within two standard deviations, and 99.7% within three standard deviations), we must figure out where 77 and 149 words per minute fall in relation to the mean (125 wpm) and standard deviation (24 wpm).
For (f), 77 words per minute is 125 - (2 × 24) = 77 wpm, which is two standard deviations below the mean. So, the Empirical Rule tells us that 95% of the data falls within two standard deviations of the mean. Since we're looking at one side of the distribution, we split the remaining 5% into two, leaving 2.5% below two standard deviations. Therefore, the proportion of students who read less than 77 words per minute is 2.5%.
For (g), 149 words per minute is 125 + (1 × 24) = 149 wpm, which is one standard deviation above the mean. According to the Empirical Rule, 68% of data falls within one standard deviation. Since we're looking for the proportion that read more than 149 words per minute, we need to look at the upper tail beyond one standard deviation. That leaves us with 100% - 68% = 32%, but since we're only interested in the half above the mean, we halve that to get 16%. Therefore, 16% of the students read more than 149 words per minute.