Question

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 850 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 standard deviation of log (to the base 10) of X? Please report your answer in 3 decimal places.

Step 1

**Introduction:**

According to the question, *X* follows the log-normal distribution. *P* (*X* > 850) = 0.5; *P* (*X* > 100) = 0.9.

The natural logarithm (base *e*) of the log-normally distributed random variable with parameters *µ* and *σ*, has a normal distribution with mean *µ* and standard deviation *σ*. Let *Y* = ln (*X*).

Now, it is known that if log* _{a}*(

Step 2

**Calculation:**

Step 3

**Calculation continued:...**

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