For a certain river, suppose the drought length Y is the number of consecutive t

Question

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 = 0.372 for this random variable. (Round your answers to three decimal places (b) What is the probability that the length of a drought exceeds its mean value by at least one standard deviation? 0.098

Explanation / Answer

here mean =1/p =1/0.372 =2.688

std deviation =((1-p)/p2)1/2 =2.1303

hence probability =P(X>2.688+2.1303)=P(X>4.82) =(1-0.372)4=0.156

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