How to Calculate and Solve for Standard Normal Variable | Probability

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.

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.