## Dataset Overview

To illustrate, weâ€™ll use a sample dataset as an example. For instance, the following dataset specifies the **Mean **and **Standard Deviation**.

## Introduction to Normal Distribution

The **Normal Distribution **is also known as a **Bell Curve**. The theory is based on the idea that the distribution of values mainly clusters around an average. Still, very high and very low values are possible in certain cases. But they are rare compared to the ones closer to the average.

### Method 1 – **Using NORMINV Function**

- The
**NORMINV**function generates the inverse of the normal cumulative distribution. - Specify the mean and standard deviation as arguments.
- Follow these steps:
- Select cell
**D5**.

- Select cell

`=NORMINV(RAND(),$B$5,$C$5)`

- Press
**Enter**. - Use the AutoFill tool to generate
**4**more numbers.

- Here,
**B5**represents the**Mean**, and**C5**represents the**Standard Deviation**. The probability is input using the**RAND**function.

### Method 2 – **Excelâ€™s NORM.INV Function**

- This method is similar to Method 1, but more compatible with recent Excel versions.
- Steps:
- Select cell
**D5**. - Enter the formula:

- Select cell

`=NORM.INV(RAND(),$B$5,$C$5)`

- Press
**Enter**. - Use
**AutoFill**to fill the series.

**Â B5 **represents the **Mean **and **C5 **denotes the** Standard Deviation. **We utilize the **RAND** function to generate the necessary probability for this parameter.

### Method 3 – **Box Muller Method**

In this method, weâ€™ll create a formula combining different Excel functions to apply the **Box Muller **method.

- Select cell
**D5**. Enter the formula:

`=SQRT(-2*LN(RAND()))*COS(2*PI()*RAND())*$C$5+$B$5`

- Press
**Enter**and use**AutoFill**to fill the series.

**How Does the Formula Work?**

**RAND() –**The**RAND**function generates random numbers.

**LN(RAND() –****The LN function**returns the natural logarithm of the numbers returned by the**RAND**function.

**COS(2*PI()*RAND() –****The COS function**returns the cosine of**2*PI()*RAND()**.

**SQRT(-2*LN(RAND()))*COS(2*PI()*RAND())*$C$5+$B$5 –**T**he SQRT function**returns random numbers.

### Method 4 – **NORM.DIST Function**

In our previous method, we’ll employ the **NORM.DIST** function to generate random numbers. This function yields values following a **normal distribution**, but it necessitates specifying the mean and the standard deviation. Therefore, acquaint yourself with the ensuing steps to generate random numbers.

**STEPS:**

- Select cell
**E5**. - Then, enter the formula:

`=NORM.DIST(B5,$C$5,$D$5,TRUE)`

- Press
**Enter**. - Use
**AutoFill**to return**4**more numbers.

We generate the normally distributed random number for each mark in the **B** column.

**Download Practice Workbook**

You can download the practice workbook from here:

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