Can someone answer a,b, and c? I want to use these as a reference to study as to getting the answer for questions like these.

section II: Free Response: Show all your work. Clearly indicate the methods you use, because you will be scored on the correctness of your methods as well as on the accuracy and completeness of your results and explanations. 1 1. A game warden claims that in a certain large lake 40% of the fish must be thrown back because they are too small to keep. Assume for now that this claim is true. Suppose that a researcher selects a random sample of 10 fish from the lake. Let Y = the number of fish that are too small to keep. (a) Explain why Y is a binomial random variable. success . Fish is for small Failure: Fish isn't too small Ii one fish that is too small doesn't affect the next fish (chance of getting either kind N: 1 = 10 5 . P=0.4 (b) Find the probability that at most 2 of the 10 fish are too small to keep, if the game warden's claim is true. 10 - 2 P (X = 2 ) = ( , (0.4 ) ( 1 - 0.4 ) (c) Suppose that 2 of the researcher's 10 randomly selected fish are too small to keep. Does this give convincing evidence that the game warden's claim is incorrect? 2