# Z-Score Probability Calculator

**Created By :** Vaibhavi Kumari

**Reviewed By :** Rajashekhar Valipishetty

**Last Updated :** Apr 10, 2023

We can guarantee you that you can easily find the probability of z-score by taking the help of the z-score probability calculator. The thing is you need to provide the input values of mean and standard deviation and then you need to press the calculate button to get the best results in less time.

## Z-Score Probability Solutions

### Z-Score Probability Formulas

To determine the z-score, we need to use some formula by using standard deviation and mean. Let us see the formula below.

**z = (x - μ) / σ**

probability values.

- Right-tailed z-test: p-value = P(x > x1) = 1 - P(x < x1)
- Left-tailed z-test: p-value = P(x < x1)

Where,

x is the random number (or) raw data point.

z is the z-score value.

μ is the mean.

σ is the standard deviation.

### Steps to Calculate the Z-Score Probability

Here are some basic steps to calculate the z-score easily and manually.

- Let us consider the data which is given in the problem.
- Then you need to calculate the mean and standard deviation.
- Then you need to apply the formula to find a z-score.
- Finally, by simplifying it you will get the result, and then from the z - table calculate the probability of z-score.

### How to Find Z-Score Probability Manually ?

**Example: In a class 3 students scored 63,87,47. Find the z-score probability of 63?**

**Solution:**

Given scores, 63, 87,47.

Find the mean and standard deviation of the scores.

μ = (67+87+47)/3 = 67.

σ = √((67-67)^2 + (87-67)^2 + (47-67)^2)/3= 28.284

Here, x = 63.

Now, apply the formula, **z = (x - μ) / σ**

z = (63 - 67)/28.284 = -4/28.28 = -0.14.

By using Z-score table, P(x < x1) = 0.4443, P(x > x1) = 1- P(x < x1) = 1- 0.443 = 0.9557

Utilize our probability calculators to complete your assignments easily that are available at probabilitycalculator.guru.

### FAQs on Z-Score Probability Calculator

**1. What is Z-Score Probability?**

z-score estimates the distance between the mean and observation. The z-score value may be negative or positive.

**2. How do you find the probability of Z-Score?**

Probability of Z- score for right tailed and left tailied is found by using the formula. Right-tailed z-test: p-value = P(x > x1) = 1 - P(x < x1), Left-tailed z-test: p-value = P(x < x1).

**3. What is the best website for the z-score probability calculator?**

Probabilitycalculator.guru is the best website for z-score probability calculator.