Final answer:
To find the probability of passing the test with at least a 70 percent, we need to determine the number of questions the student needs to answer correctly. Since the test has 30 questions, 70 percent of 30 is 21. So the student needs to answer 21 or more questions correctly to pass.
Step-by-step explanation:
To find the probability of passing the test with at least a 70 percent, we need to determine the number of questions the student needs to answer correctly. Since the test has 30 questions, 70 percent of 30 is 21. So the student needs to answer 21 or more questions correctly to pass.
Since the student is guessing randomly, each question has a 50 percent chance of being answered correctly (true or false). So the probability of answering any given question correctly is 0.5.
To find the probability of answering 21 or more questions correctly, we can use the binomial probability formula. The formula is:
P(X >= k) = 1 - P(X < k)
where P(X >= k) is the probability of getting k or more successes, P(X < k) is the probability of getting less than k successes, and k is the number of successes.
In this case, the number of trials (n) is 30, the probability of success (p) is 0.5, and the number of successes (k) is 21. Plugging these values into the formula, we get:
P(X >= 21) = 1 - P(X < 21)
Using a binomial probability calculator or table, we can find the probability of getting less than 21 successes. Subtracting this probability from 1 gives us the probability of getting 21 or more successes, which is the probability of passing the test with at least a 70 percent.