# How to find z score for percentile

To find z score for percentile, we check the percentile value in the center part of the normal distribution table. For example, find the z score of the 45th percentile.

## The Z score for the 45th percentile is -0.13

Example two, find the z score of the 33rd percentile. The Z score for the 33rd percentile is -0.44

## Percentile to z score formula

The formula of percentile to z score formula assumes that the underlying distribution is normal. The formula to calculate percentile to z score is given by; Where T is the percentile

Notably, we can find the value of the z score of a percentile in excel using the excel function =Norm.Inv (T,0,1)

Where T is the percentile

0 is the standard mean

1 is the standard deviation

For example, consider the 40th Percentile, and find the z score in excel. Thus, the value will be; The Z-score for the 40th percentile is -0.25335

## Examples to find z score for percentile

### What z score represents the 95th percentile

The z-score that represents the 95th Percentile is 1.645

### What z score represents the 90th percentile

The z-score that represents the 90th Percentile is 1.282

### What z score represents the 80th percentile

The z-score that represents the 80th Percentile is 0.842

### What z score represents the 75th percentile

The z-score that represents the 75th Percentile is 0.674

### What z score represents the 85th percentile

The z-score that represents the 85th Percentile is 1.036

### What z score represents the 20th percentile/2nd decile

The z-score that represents the 20th Percentile is -0.842

## Z score percentile table/chart

 Percentile Z-Score Percentile Z score 1 -2.326 51 0.025 2 -2.054 52 0.05 3 -1.881 53 0.075 4 -1.751 54 0.1 5 -1.645 55 0.126 6 -1.555 56 0.151 7 -1.476 57 0.176 8 -1.405 58 0.202 9 -1.341 59 0.228 10 -1.282 60 0.253 11 -1.227 61 0.279 12 -1.175 62 0.305 13 -1.126 63 0.332 14 -1.08 64 0.358 15 -1.036 65 0.385 16 -0.994 66 0.412 17 -0.954 67 0.44 18 -0.915 68 0.468 19 -0.878 69 0.496 20 -0.842 70 0.524 21 -0.806 71 0.553 22 -0.772 72 0.583 23 -0.739 73 0.613 24 -0.706 74 0.643 25 -0.674 75 0.674 26 -0.643 76 0.706 27 -0.613 77 0.739 28 -0.583 78 0.772 29 -0.553 79 0.806 30 -0.524 80 0.842 31 -0.496 81 0.878 32 -0.468 82 0.915 33 -0.44 83 0.954 34 -0.412 84 0.994 35 -0.385 85 1.036 36 -0.358 86 1.08 37 -0.332 87 1.126 38 -0.305 88 1.175 39 -0.279 89 1.227 40 -0.253 90 1.282 41 -0.228 91 1.341 42 -0.202 92 1.405 43 -0.176 93 1.476 44 -0.151 94 1.555 45 -0.126 95 1.645 46 -0.1 96 1.751 47 -0.075 97 1.881 48 -0.05 98 2.054 49 -0.025 99 2.326 50 0

## What is a percentage rank?

Percentile rank (PR) of a given score in statistics refers to the proportion of scores lower than a given score in a frequency distribution.

To make the meaning of test results more understandable, percentile ranks are frequently used.

According to the test theory, the percentile rank of a raw score is understood to be the proportion of test-takers in the norm group who received a score lower than the score of interest.

Statistics professionals frequently use percentile rank to determine how an individual assessment score or outcome relates to others in a set.

Additionally, knowing the percentile rank can help one gain perspective on how well they did on a particular test.