Question

a) The flow in a river can be modeled as a log-normal distribution. From the data, it was estimated that, the probability that the flow exceeds 855 cfs is 50% and the probability that it exceeds 100 cfs is 90%. Let X denote the flow in cfs in the river. Flood conditions occur when flow is 5000 cfs or above. To compute the percentage of time flood conditions occur for this river, we have to find, P(X≥5000)=1-P(Z<a). What is the value of a? Please report your answer in 3 decimal places.

b) What is the probability of P(Z<2.23)? Please report your answer in 3 decimal places.

Answer 1

The flow in a river can be modeled by Log - Normal Distribution .

................ where are parameters of lognormal distribution   

Also , we know that :

.......... Standard Normal Distribution

Our first aim is to find the value of   .

For this , we are given two conditions :

• Probability that flow exceeds 855 cfs is 50 %
• Probability that flow exceeds 100 cfs is 90 %

Using Standard Normal Distribution Tables :

............................. ( * )

.......................Since , P ( Z > z ) = 1 - P ( Z < z )

....................... Since , P ( Z < - z ) = P ( Z > z )

Using Standard Normal Distribution Tables :

................. Using ( * )

• Using Standard Normal Distribution Tables :