Question

Suppose that stream flows for a particular river are normally distributed about a mean stream flow of 85,000cfs with a standard deviation of 3200cfs. Documented flooding issues occur along this river when stream flows exceed 102000cfs. What is the probability that over a three year period flooding will occur twice within this river?

Answer 1

the given informations are mean=85000, sd=3200 ( please check the standard deviation , it may be 32000)

here we use standard normal variate z=(x-mean)/sd

for x=102000, z=(102000-85000)/3200=5.3125

P(flooding in a given year)=p=P(X>102000)=P(Z>5.3125)=1-P(Z<5.3125)=1-0.9999=0.0001

now we use binomial distribution with parameter n=3 and p=0.0001 and for

Binomial distribution ,P(X=r)=ⁿC_rp^r(1-p)^n-r  

P(X=2)=³C₂p0.0001²(1-0.0001)^3-2 =0.0000

if standard deviation is 32000 then for x=102000, z=(102000-85000)/32000=0.5313

P(X=2)=³C₂p0.5313²(1-0.5313)^3-2 =0.3969