Z score estimates the number of standard deviations within a set of data that is above or below the sample mean. This online Z score calculator calculates the z score by subtracting the mean from the variable and dividing it by the standard deviation.

X = Standardized Random Variable,

$\mu$ = Population mean,

s = Population Standard Deviation.

**Z score Formula:**$z = \frac{X - \mu }{s}$

Where,X = Standardized Random Variable,

$\mu$ = Population mean,

s = Population Standard Deviation.

**Step 1:**Note down the given data.

**Step 2:**Plug in the data value into the z score formula given above and get the z score.

Let's discuss some of the problems based on z score.

### Solved Examples

**Question 1:**The grades on a final exam of zain are normally distributed with $\mu$ = 97 and s = 3.5. Zain scored 95 on the exam. Find the z score for zain's exam grade.

**Solution:**

Step 1 :

Given data, $\mu$ = 97, s = 3.5 , X = 95, z = ?.

Step 2 : z score of zain is,

z = $\frac{X - \mu }{s}$

z = $\frac{95 - 97 }{3.5}$

z = $\frac{-2}{3.5}$

z = -0.57

Therefore, Zain's score was -0.57 standard deviation below the sample mean.

**Question 2:**In a cadbury factory, the weight of dairy milk has a mean of 9 ounces with 0.2 ounce as standard deviation. Find the z score corresponding to weight of 9.7 ounces.

**Solution:**

Step 1 :

Given data, $\mu$ = 9, s = 0.2 , X = 9.7, z = ?.

Step 2 : z score of dairy milk is,

z = $\frac{X - \mu }{s}$

z = $\frac{9.7 - 9}{0.2}$

z = $\frac{0.7}{0.2}$

z = 3.5

Therefore, dairy milk's weight was 3.5 standard deviation above the sample mean.