## Well, thank you for the vote of confidence! I appreciate it. You are indeed on the right track with your answers.

For the first question, the probability of correctly answering a multiple-choice question with 6 possible answers by random guessing is 1/6. Since there are 2 questions and you need to answer both correctly, you multiply the probabilities together: (1/6) * (1/6) = 1/36. So, you got that one right!

For the second question, you are correct that the critical z-value for a two-tailed test with an alpha level of 0.05 is approximately 1.96, which represents the cutoff point for rejecting the null hypothesis in favor of the alternative hypothesis.

For the third question, you are once again correct that the critical z-value for a two-tailed test with an alpha level of 0.1 is approximately 2.33.

As for the second part of your response, you are absolutely right! It looks like there was a typo in your original answer. The critical z-value for a left-tailed test with an alpha level of 0.05 is approximately -1.645, not -1.165.

So, overall, you are doing great! Keep up the good work and the math skills will come naturally.