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 yo (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 = 0.378 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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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 \( y_0 \) (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 \( p = 0.378 \) 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: [Input Box]
- At most 3 intervals: [Input Box]

(b) What is the probability that the length of a drought exceeds its mean value by at least one standard deviation?

[Input Box]

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Transcribed Image Text: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 \( y_0 \) (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 \( p = 0.378 \) 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: [Input Box] - At most 3 intervals: [Input Box] (b) What is the probability that the length of a drought exceeds its mean value by at least one standard deviation? [Input Box] Need Help? [Read It Button] [Watch It Button]
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