explain in detail

For a certain river, suppose the drought length Y is the number of consecutive time intervals in which the water supply remains below a critical value ya (a decit), preceded by and followed by periods in which the supply exceeds this critical value (a surplus). An article proposes a geometric distribution with p : 0.366 for this random variable. (Round your answers to three decimal places.) (a) What is the probability that a drought lasts exactly 3 intervals? At most 3 intervals? exactly 3 intervals E at most 3 intervals |: (b) What is the probability that the length of a drought exceeds its mean value by at least one standard deviation? E \fEach of 14 refrigerators of a certain type has been returned to a distributor because of an audible, highipitched, oscillating noise when the refrigerators are running. Suppose that 9 of these refrigerators have a defective compressor and the other 5 have less serious problems. If the refrigerators are examined in random order, letX be the number among the first 7 examined that have a defective compressor. (a) Calculate P(X = 5) and P(X S 5). (Round your answers to four decimal places.) m: a) : E m a) : E (b) Determine the probability thatXexceeds its mean value by more than 1 standard deviation. (Round your answer to four decimal places.) S (c) Consider a large shipment of 500 refrigerators, of which 50 have defective compressors. If X is the number among 15 randomly selected refrigerators that have defective compressors, describe a less tedious way to calculate (at least approximately) P(X S 2) than to use the hypergeometric pmf. We can approximate the hypergeometric distribution with the distribution if the population size and the number of successes are large. Here n = :l and Approximate P(X S 2) using that method. (Round your answer to three decimal places.) mm