The flow in a river can be modeled as a log-normal distribution. From

meplasemamiuk

meplasemamiuk

Answered question

2021-12-03

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 821 cfs is 50% and the probability that it exceeds 100 cfs is 90%. Let X denote the flow in cfs in the river. What is the mean of log (to the base 10) of X? Please report your answer in 3 decimal places.

Answer & Explanation

Michele Tipton

Michele Tipton

Beginner2021-12-04Added 11 answers

Step 1
In this question, it has been given that the flow in a river is modeled as the log normal distribution, the probability that the flow exceeds 821 cfs is 50% and the probability that flow exceeds 100 cfs is 90%. Using the given information, we have to find the mean of log of X.
Step 2
Since in the question it has mentioned that the probability that flow is greater than 821 is 0.50 which ultimately means probability that flow is less than 821 is 0.50.
Also, the probability that flow is greater than 100 cfs is 0.90 which means the probability that X is less than 100 cfs is 0.10.
P(log(x)<log(821))=0.50 (1)
P(log(x)<log(100))=0.10 (2)
Using the equation (1)
P(log(x)μσ<log(821)μσ)=0.50
log(821)μσ=0
log(821)μ=0
μ=log(821)
μ=2.91434
Step 3
Answer: 2.91434

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