Suppose you have a quiz consisting of 25 multiple-choice questions, with each question having one correct answer out of the four possible selections. Further assume that someone is taking the test based purely on guessing the correct answer.
a) Justify why the number of correctly guessed answers can, or cannot, be modeled with a binomial distribution. Be specific on how this scenario either does or does not satisfy the requirements for a binomial experiment.
b) If it can be modeled with a binomial distribution, then specify the values for the probability of success and the probability of failure, where the random variable records the number of correct guesses.
c) Find the probability someone guesses at least 13 answers correctly.
d) Find the probability that someone guesses no more than 5 of the answers correctly.
e) Find the probability that someone guesses exactly 6 of the answers correctly.
f) Find the probability that someone guesses at least 3, but no more than 9, of the answers correctly.
g) How many correct answers would you expect some to guess? Label this value using the appropriate symbol.
h) Compute the standard deviation and variance for the number of answers guessed correctly.
i) Label each using the appropriate symbol.