In one of its Spring catalogs, L. L. Bean® advertised footwear on 28 of its 192 catalog pages. Suppose we randomly survey 20 pages. We are interested in the number of pages that advertise footwear. Each page may be picked more than once. Part (a) In words, define the random variable X. the number of pages in the catalog the number of pages we must survey until we find one that advertises footwear the number of pages that advertise footwear the number of footwear styles the number of times a page could be picked Part (b) List the values that X may take on. X = 0, 1, 2, ..., 192 X = 1, 2, ..., 28 X = 1, 2, ..., 20 X = 0, 1, 2, ..., 20 X = 0, 1, 2, ..., 28 Part (c) Give the distribution of X. (Enter exact numbers as integers, fractions, or decimals.) X ~ ? , Part (d) How many pages do you expect to advertise footwear on them? (Round your answer to the nearest whole number.) 3 Part (e) Is it probable that all twenty will advertise footwear on them? Why or why not? (Round your answer to two decimal places.) No , because the probability that all twenty will advertise footwear is . Part (f) What is the probability that fewer than eight will advertise footwear on them? (Round your answer to four decimal places.) Part (g) Reminder: A page may be picked more than once. We are interested in the number of pages that we must randomly survey until we find one that has footwear advertised on it. Define the random variable X. the number of pages in the catalog the number of pages we must survey until we find one that advertises footwear the number of pages that advertise footwear the number of footwear styles the number of times a page could be picked Give its distribution. (Enter an exact number as an integer, fraction, or decimal.) X ~ ? Part (h) What is the probability that you only need to survey at most five pages in order to find one that advertises footwear on it? (Round your answer to four decimal places.) Part (i) How many pages do you expect to need to survey in order to find one th