z score finder :

This calculator is used to find the z score of a normal distribution with detailed solution.

Z-score and Probability Converter :

This calculator convert the z-score into the probability. just select the Conversion Type, enter the Z-scores and get Instant Results with detailed solution.

Two-Tailed:

\( \le \mathrm{Z} \le \)

Left-Tailed:

\( \mathrm{Z} \le \)

Right-Tailed:

\( \mathrm{ Z } \ge \)

Type-4:

\( \mathrm{ | Z | \le } \)

Type-5:

\( \mathrm{ | Z | \ge } \)

z-score formula :

The Z-score is also known as a standard score which is a statistical measurement that describes a data point's position relative to the mean of a group of data points. The Z-score indicates how many standard deviations an element is from the mean.

The formula for the z-score is \( \mathrm{ z = \frac{x-\mu}{\sigma}} \)

In this formula

x is the value of the data point.
\(\mu\) is the population mean average of the data points.
\(\sigma\) is the population standard deviation of the data points.

Uses of the Z-score :

It standardise various datasets to a similar scale to make comparisons easier.
It help identify outliers, if z-csore is beyond \( \pm 3 \) it can be considered as outlier.
In a normal distribution, the Z-scores can be used to determine the probability of a value occurring within a certain range.

How to find probability

The probability can be obtained using various method includes Excel function, r-code or using z-table also known as standard normal distribution table.

Standard normal distribution table

The tables below represent the area to the left of the given Z-score.

left tailed probability for positive z-score :

left tailed probability for negative z-score :

Step to Find the p-value from a Z-table

Locate the row that corresponds to the first digit of your z-score.

Example: For a z-score of 1.23, find the row for 1.2.

Locate the column that corresponds to the second digit of your z-score.

Example: For a z-score of 1.23, find the column for 0.03.

The intersection of the row and column will give you the p-value for that z-score.

Example: The intersection of row 1.2 and column 0.03 will give you the p-value for a z-score of 1.23.

Frequently Asked Questions :

are standardized scores and z scores the same thing

Yes, standardized scores and z-scores generally refer to the same concept in statistics.

how to find z score from area

To find z score from area used our Z-score and Probability Converter for easy understanding