Final answer:
To find the probability of passing with at least 70 percent on a 10-question true-false quiz when guessing, you would use the binomial distribution to calculate the probabilities for getting 7, 8, 9, or 10 questions correct and sum those probabilities.
Step-by-step explanation:
The question poses a scenario in which a student takes a 10-question true-false quiz and guesses on each question. The task is to calculate the probability that the student will pass the quiz with at least a 70 percent score, meaning the student must get at least 7 out of 10 questions correct.
For each question, there is a 50 percent chance of guessing correctly, since it's a true-false question. Therefore, the probability of guessing exactly 7 correct answers is a binomial probability problem, which can be solved using the binomial formula or by using a binomial probability distribution table. The same process can be repeated to calculate the probability of getting exactly 8, 9, and 10 correct answers. The overall probability of passing the quiz with at least a 70 percent is the sum of these probabilities.
This kind of problem is an example of applications of binomial distribution and is common in high school level probability and statistics.