Zhanyu is hunting for the rare four-leaf clover. He is hunting in a location known to produce four-leaf clovers at an unusually common frequency of 1 four-leaf clover out of every 400 clovers examined. Each clover will have four leaves independent of all other clovers. a) If F is the random variable denoting the number of four-leaf clovers Zhanyu finds in a clover patch with exactly 1235 clovers. Determine the distribution, parameter(s), and support of F. b) Determine the probability that Zhanyu finds between 2 and 4 (inclusive) four-leaf clovers in the patch. c) Zhanyu wants to find 3 four-leaf clovers to give to his friends. Determine the minimal size of the patch necessary for Zhanyu to examine such that he can be 95% sure that he will find 3 four-leaf clovers. d) Zhanyu has gathered a group of friends to help him search a larger clover patch. In this clover patch there are exactly 3 thousand clovers. Let F represent the random variable that approximates this distribution. Mathematically justify your approximation and state the approximating distribution and its parameter(s). e) Use the approximating distribution from d) to find the probability that Zhanyu finds fewer than 5 four-leaf clovers in the large clover patch.