Question: 5. A student randomly guesses on a five question multiple choice exam (and hence independence betweeneach question can be assumed). The probability of correctly guessing

5. 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 = np and 2 = np(1 p), respectively.Determine the mean and variance of X.

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