Suppose a reading between 30 and 40 is called very interesting from an archaeological point of view. Let us say you take readings at n=12 sites chosen at random. Let r be a binomial random variable that represents the number of "very interesting" readings from these 12 sites. a) Let us call "very interesting" a binomial success. Probability of success on a single trial, where p-P(success) - p(30 less than or equal to x less than 40). b) What is the expected value p and standard deviation for the random variable r? c) What is the probability that you will find at least one "very interesting" reading in the 12 sites? d) What is the probability that you will find fewer than three "very interesting" readings in the 12 sites?