A student randomly guesses on a five question multiple choice exam (and hence independence betweeneach question can be assumed). The probability of correctly guessing each question is 0.2. Let X be the random variable for the number of correct guesses.
(i) Explain why this scenario follows a binomial probability model.
(ii) Determine the probability of answering exactly 3 questions correctly.
(iii) Determine the probability of answering at most 2 questions correctly.
(iv) The mean and variance of a binomial random variable is µ = np and σ2 = np(1 - p), respectively.Determine the mean and variance of X.