A multiple-choice examination consists of 95 questions, each having possible choices a, b, c, d, and e. Approximate the probability that a student will get fewer than 22 answers correct if she randomly guesses at each answer. (Note that, if she randomly guesses at each answer, then the probability that she gets any one answer correct is 0.2) Use the normal approximation to the binomial with a correction for continuity.
Round your answer to at least three decimal places. Do not round any intermediate steps.