Answer:
a. The probability of guessing correctly for any individual question is 1/4, since there are four response choices and only one of them is correct.
b. On average, a student would answer 8 questions correctly for the entire test by guessing. This is because there are 32 questions and each question has a 1/4 chance of being answered correctly, so 32 x 1/4 = 8.
c.To calculate the probability of a student getting more than 12 answers correct simply by guessing, we need to use the binomial distribution formula. The formula is:
P(X > k) = 1 - Σ P(X = i), i = 0 to k
where P(X > k) is the probability of getting more than k correct answers, P(X = i) is the probability of getting exactly i correct answers, and Σ represents the sum from i = 0 to k.
In this case, k = 12, since we want to find the probability of getting more than 12 correct answers. The probability of getting exactly i correct answers can be calculated using the binomial distribution formula:
P(X = i) = C(32, i) * (1/4)^i * (3/4)^(32-i)where C(32, i) is the number of ways to choose i correct answers out of 32 questions.
By plugging in the values into the first formula, we can find that the probability of a student getting more than 12 answers correct simply by guessing is approximately 0.097 or 9.7%. This means that a student has a relatively low chance of getting more than 12 answers correct by simply guessing on the test.