Final answer:
The probability of a student guessing more than 75 percent of the answers correctly on a 32-question multiple choice exam is virtually zero.
Step-by-step explanation:
The question concerns calculating the probability that a student who has not studied for a 32-question multiple choice exam, with each question having three possible answers, will guess more than 75 percent of the questions correctly. More than 75 percent of 32 questions would mean the student has to guess more than 24 questions correctly. To calculate the probability of the student guessing more than 24 questions correctly (P(x > 24)), we can use the complement of the probability of guessing 24 or fewer questions correctly. Utilizing a calculator's distribution function, we find that the probability is virtually zero or P(x > 24) = 0, as it is improbable to guess such a high number of questions correctly by chance.