In Minecraft speedruns players compete to complete the video game Minecraft as quickly as possible. A runner needs a certain number of ender pearls and blaze rods to access the end portals (a step in finishing the game.) Blaze rods are won by fighting blazes (a game creature). Upon being killed, each blaze has a 50% chance of dropping one blaze rod. To obtain ender pearls runners use a game mechanic known as bartering: In a barter, the player exchanges a gold ingot with a piglin (a game creature) for a randomly generated item. For each barter, there is a 20 423 0.0473 chance (in Mindcraft 1.16.1) the piglin will give the player ender pearls for the ingot. An analysis of speedruns by player Dream showed that 42 of the 262 piglin barters performed throughout these streams yielded ender pearls and 211 of the 305 killed blazes dropped blaze rods. Let Xrods be the random variable giving the number of blaze rods obtained after fighting 305 random blazes and Xpearls the number of times ender pearls were obtained in random 262 piglin barters. Assume independence of barters and blaze rod drops. The probability p = P(Xpearls 42 and Xrods 211) can be considered a measure of how unlikely Dreams results in an unmodified game would be.

(a) Determine the distribution of Xrods and its parameters. (1p) (b) Determine a normal approximation to Xrods. (1p) (c) Assume P(Xpearls 42) = 5.65 1012. Use the normal approximation to compute p (approximately). (2p) (d) Formulate a null-hypothesis and an alternative hypothesis (in words) for which p is a proper p-value. What is your conclusion for the corresponding test at significance level = 1%?