Final answer:
The probability of passing the quiz with at least a 70 percent can be determined using the binomial probability formula for each possible number of correct guesses required to pass and summing these probabilities. Predicting a final exam score based on a previous high score is speculative but may indicate a similar outcome. Larger sample sizes in experiments are typically better, making statement 8 true, while statement 7 about human experimentation is false with proper ethical procedures.
Step-by-step explanation:
To determine the probability of a student passing a test with at least 70 percent, we must calculate the chance of the student guessing enough correct answers on a true-false quiz. The student needs to get at least 7 out of 10 questions correct to achieve a 70 percent. The probability of guessing one question correctly is 1/2, since there are two possible answers. Because each question is independent, the probability of guessing exactly 7 right is given by the binomial probability formula, which in this case is C(10, 7) * (1/2)^7 * (1/2)^(10-7), where C(n, k) represents the number of combinations of n items taken k at a time. The same calculation must be done for guessing 8, 9, or all 10 right and then summing those probabilities to find the total probability of passing the quiz.
Concerning predicting the final exam score based on a student's third exam score of 90, it's a subjective prediction. However, using historical data, a professor might predict that the student is likely to maintain a similar grade. Finally, in experiments and statistics, larger sample sizes are generally preferable because they provide more data for analysis and can lead to more reliable conclusions, thus true for statement 8 about sample sizes in experiments. Question 7 is more nuanced; although there are ethical considerations and regulations to adhere to, experiments can be done on humans with the proper oversight and consent, so this statement can be considered false.