The image above represents standard normal variable. To calculate the probability of standard normal variable, three essential parameters are needed and these parameters are **value (x), mean (μ) **and **standard deviation (σ).**

The formula for calculating standard normal variable:

z = ^{(x – μ)} ⁄ _{σ}

Where;

z = Standard Normal Variable

x = Value

μ = Mean

σ = Standard Deviation

Let’s solve an example;

Find the standard normal variable when the value is 4, the mean is 20 and the standard deviation is 26.

This implies that;

x = Value = 4

μ = Mean = 20

σ = Standard Deviation = 26

z = ^{(x – μ)} ⁄ _{σ}

So, z = ^{(4 – 20)} ⁄ _{26}

z = ^{(-16)} ⁄ _{26}

z = -0.615

Therefore, the **standard normal variable** is **-0.615.**

**Calculating for Value when the Standard Normal Variable, the Mean and the Standard Deviation is Given**

x = zσ + μ

Where;

x = Value

z = Standard Normal Variable

μ = Mean

σ = Standard Deviation

Let’s solve an example;

Find the value when the standard normal variable is 12, the mean is 10 and the standard deviation is 4.

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This implies that;

z = Standard Normal Variable = 12

μ = Mean = 10

σ = Standard Deviation = 4

x = zσ + μ

Then, x = (12)(4) + 10

x = 48 + 10

x = 58

Therefore, the **value **is **58.**

**Calculating for Mean when the Standard Normal Variable, the Value and the Standard Deviation are Given**

μ = x – zσ

Where;

μ = Mean

z = Standard Normal Variable

x = Value

σ = Standard Deviation

Let’s solve an example;

Find the mean when the standard normal variable is 6, the value is 30 and the standard deviation is 3.

This implies that;

z = Standard Normal Variable = 6

x = Value = 30

σ = Standard Deviation = 3

μ = x – zσ

So, μ = 30 – (6)(3)

μ = 30 – 18

μ = 12

Therefore, the **mean **is **12.**

Read more: How to Calculate and Solve for Standard Deviation | Probability

**Calculating for Standard Deviation when the Standard Normal Variable, the Value and the Mean are Given**

σ = ^{x – μ} / _{z}

Where;

σ = Standard Deviation

z = Standard Normal Variable

x = Value

μ = Mean

Let’s solve an example;

Find the standard deviation when the standard normal variable is 8, the value is 40 and the mean is 8.

This implies that;

z = Standard Normal Variable = 8

x = Value = 40

μ = Mean = 8

σ = ^{x – μ} / _{z}

So, σ = ^{40 – 8} / _{8}

σ = ^{32} / _{8}

σ = 4

Therefore, the **standard deviation **is **4.**

**How to Calculate Standard Normal Variable Using Nickzom Calculator**

Nickzom Calculator – **The Calculator Encyclopedia** is capable of calculating the standard normal variable.

To get the answer and workings of the standard normal variable using the **Nickzom Calculator – The Calculator Encyclopedia. **First, you need to obtain the app.

You can get this app via any of these means:

**Web** – https://www.nickzom.org/calculator-plus

To get access to the **professional **version via web, you need to **register** and **subscribe **for** NGN 1,500 **per** annum** to have utter access to all functionalities.

You can also try the **demo **version via https://www.nickzom.org/calculator

**Android (Paid)** – https://play.google.com/store/apps/details?id=org.nickzom.nickzomcalculator

**Android (Free)** – https://play.google.com/store/apps/details?id=com.nickzom.nickzomcalculator

**Apple (Paid)** – https://itunes.apple.com/us/app/nickzom-calculator/id1331162702?mt=8

Once, you have obtained the calculator encyclopedia app, proceed to the **Calculator Map, **then click on **Probability**** **under **Mathematics****.**

Now, Click on **Standard Normal Variable**** **under **Probability**

The screenshot below displays the page or activity to enter your values, to get the answer for the standard normal variable according to the respective parameters which are the **value (x), mean (μ) **and **standard deviation (σ).**

Now, enter the values appropriately and accordingly for the parameters as required by the **value (x)** is **4**,** mean (μ) **is **20 **and **standard deviation (σ) **is **26.**

Finally, Click on Calculate

As you can see from the screenshot above, **Nickzom Calculator**– The Calculator Encyclopedia solves for the standard normal variable and presents the formula, workings and steps too.