Area to the Right of Z Calculator

This calculator finds the area to the right of z and give answer in decimal and percentage form. The calculator also provides a step-by-step solution to help you learn how to find this area using Z tables. You’ll also see a graphical representation of the shaded area to the right of z.

Simply enter a z-score and click the calculate button to get instant results with a clear, step-by-step solution now!

Do you want a one-in-all calculator that computes various cumulative probabilities from z? Use the z-score to probability calculator instead.

How to Use the Area to the Right of Z Calculator

Finding the area to the right of z using this tool is straightforward. You don’t need to use the standard normal tables. Just follow these simple steps:

• Step 1. Enter your z value
• Step 2. Click the “calculate” button

The calculator will instantly return the probability to the right of z as a decimal/percentage. It also provides a clear, step-by-step solution, explaining how you can find this area using the standard normal table. Notably, you also get to see how you can represent this area on a standard normal curve.

What is the Area to the Right of a z-score?

The area to the right of a z-score represents the probability that a value from a standard normal distribution is greater than that z-score.

The formula for finding the area to the right of z is P(Z>z)=1−Φ(z)

Where Φ(z) is the cumulative probability (area to the left) from the standard normal distribution table.

The result represents the right-tail probability under the standard normal curve.

How to Find the Area to the Right of a Z Score (Step-by-Step)

Step 1: Identify the Z Score

Start with the given z-score. This is the value that marks the boundary of the right-tail region.

Step 2: Use the Z Table

Look up the z-score in the Z table.
Remember: the Z table gives the area to the left of a z-score (Φ(z)).

Step 3: Apply the Formula

Since we want the area to the right, subtract Φ(z) from 1.

Thus, P(Z>z)=1−Φ(z)

Step 4: Interpret the Result

The result represents the probability that a value from the standard normal distribution is greater than your z-score.

Example

Question. The scores on a statistics final exam are normally distributed with a mean of 70 and a standard deviation of 8. Find the probability that a randomly selected student scores more than 82.

Solution

Step 1. Identify the Z score

We need to find P(X > 82)

From the question, we’re provided with a raw score and not a z-score. Thus, we first need to calculate the z score using the formula z = (X−μ​)/σ

We know that the raw score, X = 82, population mean, μ =70, and the population standard deviation, σ = 8

Thus, z = (82-70)/8

= 1.5

Want to quickly find z score from the raw score? Use the raw to z-score calculator

Thus, we should find P(Z > 1.5)

Step 2. Using the Z table

The z table gives the area to the left of z. Using a positive z table, find the value at the intersection of 1.5 in the row and 0 in the column. This gives 0.9332

Thus, the area to the left of z = 1.5 is 0.9332. That is, Φ(1.50) = 0.9332

Step 3. Apply the formula

We apply the formula and subtract the area to the left of z from 1.

Thus, P(Z>1.50)=1−0.9332

=0.0668

Step 4. Interpretation

The probability that a randomly selected student scores more than 82 is 0.0668 or 6.68%. In other words, about 6.7% of students will score higher than 82.

Note. The area to the right of z score calculator will also yield similar results, as shown below.

Related. How to Find Probability from Z Using Standard Normal Tables

Frequently Asked Questions