In all of William Shakespeare's works, he used 884,6475 different words. Of these, 14,376 appeared only once. In 1985 a 429-word poem was discovered that may have been written by Shakespeare. To keep the probability calculations simple, assume that the choices between a new word and one from the list of 884,647 are independent for each of the 429 words. Approximate the probability that a new word will not be on the list, by the relative frequency of words used once.
(a) Find the expected number of new words in the poem.
(b) Use the normal approximation to the binomial to determine the probability of finding 12 or more new words in the poem. Use the continuity correction.
(c) Use the normal approximation to the binomial to determine the probability of finding 2 or fewer new words in the poem. Use the continuity correction.
(d) Use the normal approximation to the binomial to determine the probability of finding more than 2 but less than 12 new words in the poem. On the basis of your answer, decide if 9 = actual number of new words not in the list is consistent with Shakespeare having written the poem or if it contradicts this claim.