Final answer:
To calculate the probability that the student gets at least 15 correct answers on a 20-question True/False quiz, use the binomial probability formula with n=20, p=0.5, and sum the individual probabilities for k=15 to k=20. The probability is approximately 0.376.
Step-by-step explanation:
To find the probability that the student gets at least 15 correct answers on a 20-question True/False quiz, we can use the binomial probability formula. Since the student is guessing randomly, the probability of getting a question correct is 0.5. The probability of getting exactly k correct answers out of n questions is given by the formula:
P(X=k) = C(n, k) * p^k * (1-p)^(n-k)
In this case, n = 20, k ≥ 15, and p = 0.5. To find the probability of getting at least 15 correct answers, we need to sum the individual probabilities for k=15, k=16, ..., k=20. Then, we can calculate the probability using this formula:
P(X ≥ 15) = P(X = 15) + P(X = 16) + ... + P(X = 20)
Using this approach, we find that the answer is approximately 0.376. Therefore, the correct option is c) 0.376.