Question 2 - Binomial probability models [Total: 8 marks] A student is about to sit a 20-question multiple choice test for STAT1122. They did not study for this particular test and hope to randomly guess the correct answer for each question without considering which choices would be more correct than others. They are hoping to pass the test. They are not sure how possible this is given that there are 6 choices to choose from for each question, where only one choice is exactly correct.

I. If this particular student blindly guesses the answer to each question, what is the probability that they will get only 10 questions correct? Let X be the total number of correct answers. X has a binomial distribution: ~Bin(n,p) [3 marks]

II. But maybe they are aiming to do better than just pass the test. So, if this particular student blindly guesses the answer to each question, what is the probability that they will get at least 11 questions correct? Let X be the total number of correct answers. X has a binomial distribution: ~Bin(n,p) [3 marks]

III. What are the 4 key assumptions that must be satisfied in order to correctly use the binomial probability distribution to answer the questions above. [2 marks]

Thankyou in advance