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 y. (a deficit), preceded by and followed by periods in which the supply exceeds this critical value (a surplus). An article proposes a geometric distribution with p = 0.363 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 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?

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