While cleaning, Tim discovers eighteen decks of standard playing cards (each deck has 52-cards composed of 13 hearts, clubs, diamonds, and spades). For this problem use the following value assignment Ace = 1, Jack = 11, Queen =12, and King = 13. a) Tim randomly selects 22 cards from one of the decks. If we let X denote the number of cards in Tim's hand that have a value greater than 5. Determine the distribution, parameter(s), and support of X. b) Determine the probability that Tim has 12 or 13 cards with a value above 5 in his hand. c) What is the expected number of cards in Tim's hand that will be at most 5? d) Tim decides to combine all eighteen decks into one pile and randomize the cards. Tim will randomly select 25 cards from the pile and will calculate a probability related to the number of those cards that are greater than 5? Is there a valid approximation that can be used to answer this question? If so, state the distribution, parameter(s) and support, along with the reason that the approximation is valid. If not, explain why not. e) If you stated that there is a valid approximation in part d) use this to find the probability that exactly 20 of the 25 selected cards have a value greater than 5. If not, use the exact distribution to compute this probability.