Formula for Z Score

Introduction to formula for Z score:

Z score is an important concept in probability.  Subtract the mean from the raw score then divided by the standard deviation is called Z score.  Standard score and Z value are also called as Z score.  In this content, we are going to illustrate about “formula for z score” with related problems. I like to share this Percentile Formula with you all through my article.

Formula for Z Score – Formula for Z Score

Formula of Z score is `Z = (x - mu)/sigma`

Mean `mu`

Standard deviation `sigma`

Example Problems – Formula for Z Score

Example problem 1 – Formula for Z score

Calculate the Z score, for the value of x is 75, mean 25 and the standard deviation 7.

Solution:

Given,

The value of x is 75

The value of mean `mu` is 25

The value of standard deviation `sigma` is 7

Already we have the formula for estimating Z score

Formula: `z = (x - mu)/sigma`

`z = (75 - 25)/7`

= `50/7`

= 7.14

The value of Z score is 7.14

Answer:  7.14

Example problem 2 – Formula for Z score

Calculate the Z score, for the value of x is 115, mean 73 and the standard deviation 20.

Solution:

Given,

The value of x is 115

The value of mean `mu` is 73

The value of standard deviation `sigma` is 20

Already, we know the formula for estimating Z score

Formula: `z = (x - mu)/sigma`

`z = (115 - 73)/20`

= `42/20`

= 2.1

The value of Z score is 2.1

Answer:  2.1


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Practicing Problems – Formula for Z Score

Practicing problem 1 – Formula for Z score

Calculate the Z score, for the value of x is 7, mean 6 and the standard deviation 6.

Answer:  0.17

Practicing problem 2 – Formula for Z score

Calculate the Z score, for the value of x is 16, mean 4 and the standard deviation 5.

Answer:  2.4