Your answer for part 1 is very good - you pick the correct histogram and give a clear reason for doing so (and clearly explain why it WOULDN’T be the other histogram). Full credit. For part 2, you say “normal,” which implies a unimodal graph with a peak in the center of the distribution. That won’t be the case here: if you look carefully at the x-axis for each distribution the peaks will end up separated (one around 8 minutes and the other around 40 minutes), whereas the center of the combined number line (around 24 minutes) has very few observations. Thus, bimodal is the description we’d be looking for here.
For part 3, your work is good - you’ve checked conditions, cited the use of the CLT, and correctly calculated the parameters of the sampling distribution. One thing - you never mention the shape (just saying “normality” as a condition isn’t equivalent to saying “the sampling distribution would be approximately normal.”). Therefore, you’d get partial instead of full credit. Advice - after citing the CLT, state that this means the sampling distribution is approximately normal.
Finally, in part 4, you’d also receive partial credit, if any. A 2-sample t-test is the correct test. However, you do not write fully correct statements for Ho and Ha. Your Ho would be that the mean travel times for the two groups are the same; Ha would be that the mean travel times for the groups are different. You only mention the ‘difference’ and do not cite it as the alternative hypothesis. Additionally, you define mu1 and mu2 as representing 50 students - but they would represent ALL students and ALL teachers at the school (since “mu” is a population parameter). I’m working on the assumption that you meant for one of your parameters to mention teachers. Be careful when typing/writing responses!
All of your answers are correct and give appropriate reasoning. A tip for part (a): when asked to make a choice in AP stats, you should explain not only why your choice is correct, but why the other option is incorrect. You could add “since histogram J is right skewed, it does not match the description” or something similar. All of your other answers are thorough, in context, and show strong understanding. Well done!
Nice job! One small thing: for #2, you’re correct in calling the shape “bimodal,” but the rubric for a similar question only gave full credit for identifying where the clusters/peaks were centered. So you’d get partial credit. Full credit: “bimodal, with peaks at around 8 minutes and 40 minutes”