Ina n extrasensory Perception (ESP) experiment, five choices are offered for each question. Assume that a person without ESP guesses randomly and thus correctly answers each question with probability, p= 1/5. Further assume that the responses are independent. Suppose that 100 questions are asked.

a. Given that X follows a binomial distribution, what are the mean and standard deviation of X?

b. Describe the distribution of p, the proportion of correct answers? What are the mean and standard deviation of p? Is it safe to assume that it is approximately normal? Explain.

c. What is the probability that a person without ESP will correctly answer at least 30 of the 100 questions? Calculate the probability using your response from part (a) as well as your response from part (b). Check if the normal distribution from part (b) gives an accurate result.