In one of its Spring catalogs, L.L. BeanR advertised footwear on 29 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.

  

a. In words, define the random variable X.

  

b. List the values that X may take on.

  

c. Give the distribution of X. X ~ _____(_____,_____)

  

d. How many pages do you expect to advertise footwear on them?

  

e. Is it probable that all twenty will advertise footwear on them? Why or why not?

  

f. What is the probability that fewer than ten will advertise footwear on them?

  

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 and give its distribution.

  

h. What is the probability that you only need to survey at most three pages in order to find one that advertises footwear on it?

  

i. How many pages do you expect to need to survey in order to find one that advertises footwear?