**NORMINV Function in Excel: Returns the inverse of the normal cumulative distribution considering two inputs - the specified mean and standard deviation.**

**What is the NORMINV function?**

The NORM.INV function **assumes a normal distribution** and returns any **P-value** on this normal distribution using a given mean and standard deviation - also called **uncertainty**.

**How to apply the NORMINV function in Excel?**

The NORM.INV function uses three inputs, of which all three are required.

- The first argument,
**probability**, is a probability corresponding to the normal distribution. Using this input, Excel is essentially being told what P-value on the normal distribution shall be returned.**Attention! Excel will return the inverse of the normal cumulative distribution!**So if we would like to determine the P90 value, we would have to use the P10 value as input for the probability since P90 is the inverse of P10. - The second argument,
**mean**, requires the arithmetic mean of the distribution. This is the**P50 energy production**value of the power plant. - The third argument,
**standard_dev**, requires the standard deviation of the distribution. This is the**energy production uncertainty**, typically higher for wind farms than for solar parks.

**How to use the NORMINV function to determine P75, P90, and any other P-value of energy production?**

Using the NORM.INV function correctly in an energy production-related context is not super intuitive - so let's see how it's done in a best practice financial model for renewable energy investments.

In the above example, we consider a wind farm with 2,400 full load hours per year. So our mean energy production on a **P50 basis is 2,400 MWh/MW - **this is the input **"mean"** for the second argument of the formula.

We also know that the **standard deviation**, here referred to as **uncertainty**, is 12%. The mean and uncertainty are all we need to determine any other P-value.

For the first argument of the formula**"probability",** Excel needs a percentage input, more precisely, **any value between 0 and 1**. In the above model, the P-value input cells have been formatted so that a **"P" **appears in front of the value, but actually, the cells only contain the numbers 50, 75, and 90.

For the P75 value, the first argument essentially reads **"(1-(75/100))". **Since Excel **returns the inverse cumulative distribution**, we need to subtract 75% from 100% to arrive at the P75 value as output.

For the second argument, **"mean"**, a simple reference to the cell containing 2,400 MWh/MW is sufficient.

The last argument, **"standard_dev", has to be converted to the same unit as the mean**. Given that the mean has been provided as an absolute input in MWh/MW, we need to multiply this mean with the 12% uncertainty in energy production.

After carefully setting up the function, Excel returns 2,206 and 2,031 MWh/MW for the P75 and P90 values, respectively.

**How to properly apply the NORMINV function in a financial model for renewable energy investments?**

Do you want to learn how to model the NORM.INV function within a financial model created explicitly for renewable energy investments? Then check out the Advanced Renewable Energy Financial Modeling course.

**Article sources**