In a scientific study, a population of 100 cats that were vaccinated against rabies were taken. Of the cats vaccinated in the scientific study, 5 acquired the disease. Suppose a pet store has 15 cats vaccinated against rabies. A customer goes to the store and buys 3 cats. Define the random variable X as the number of cats purchased by the customer that acquire rabies. a) What distribution does the variable X follow? Write the probability function. b) What is the probability that none of the cats bought at the store get the rage? c) What is the probability that 2 or more cats acquire rabies? d) What are the average and standard deviation of the dogs that acquire rabies?