Final answer:
The correct estimated percentage of new products that fail in their first year is 80 percent to 90 percent. To calculate the probability of passing a true-false quiz with at least a 70 percent score by guessing, you add up the probabilities of getting 7, 8, 9, or 10 questions right.
Step-by-step explanation:
The estimated percentage of new products that fail in their first year on the market is 80 percent to 90 percent. Now, addressing the probability question, a student is guessing on a 10-question true-false quiz aims to pass with at least a 70 percent score, which means getting at least 7 out of 10 questions correct. For a true-false question, there is a 50 percent chance of guessing correctly. To find the probability of the student passing the quiz, we calculate the probabilities of getting exactly 7, 8, 9, or 10 questions right and sum these probabilities up.
The formula for the probability of getting exactly k successes out of n trials in a binomial experiment is given by:
P(X=k) = C(n, k) * p^k * (1-p)^(n-k)
where C(n, k) is the number of combinations of n things taken k at a time, p is the probability of success on a single trial, and (1-p) is the probability of failure on a single trial.
By applying this formula and adding up the probabilities of getting 7, 8, 9, or 10 correct answers, we can find the total probability of passing the quiz.