Question: a. On a multiple choice exam there are 30 questions and each question has 5 possible choices. There is only 1 correct answer and 4 incorrect answers for each question on the exam. If \(p=P(\) incorrect ) and \(q=P(\) correct), calculate \(\mu, \sigma^{2}\) and \(\sigma\) for this binomial experiment.

b. Suppose a student makes a random guesses on each of the 30 questions on the exam. If the student gets 23 questions incorrect, is this an unusual number of incorrect answers? Use the mean and standard deviation from part a. Explain your answer.

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