Final answer:
To find the minimum score the instructor can set so that the probability that a student will pass just by guessing is 20% or less, we need to determine the number of questions the student needs to answer correctly to pass.
Step-by-step explanation:
To find the minimum score the instructor can set so that the probability that a student will pass just by guessing is 20% or less, we need to determine the number of questions the student needs to answer correctly to pass. In this case, a passing grade is at least 70% of the questions correct. Since the student is randomly guessing on each question, the probability of guessing a question correctly is 1/2 for a true-false quiz or 1/3 for a multiple choice exam.
For a 10-question true-false quiz, the student needs to answer at least 7 questions correctly to pass. The probability of guessing 7, 8, 9, or all 10 questions correctly can be calculated using binomial probability:
For a 32-question multiple choice exam, the student needs to answer at least 23 questions correctly to pass. The probability of guessing 23, 24, 25, or all 32 questions correctly can also be calculated using binomial probability:
Therefore, the minimum score the instructor can set so that the probability of passing just by guessing is 20% or less would depend on the number of questions on the quiz or exam and the probability of guessing the correct answer. Based on the given answer choices (a) 25%, (b) 30%, (c) 15%, and (d) 10%, we would need more specific information about the number of questions and the probability of guessing correctly to determine the correct option.