Definition: -A z score is the number of standard deviation that a value of x, is above or below the mean.
Note:-f the value of x is less than the mean, the z score is negative; if the value of x is more than the mean, the z score is positive, and if the value of x equals the mean, the associated z score is zero.
Z score formula:-
Z score formula for x= (x- µ)/σ
Z score formula for x? = (x? -µ)/( σ/√n)
Where,
µ= Population mean
σ= Population standard deviation
n= sample size.
Example: - Let x be a continuous random variable that has a normal distribution with a mean of 50 and a standard deviation of 10. Convert the following x values to z values.
1) X= 55
2) x=35
Solution:- For the given normal distribution, µ=50 and σ=10.
1) The z score for x=55 is computed as follows:
Z= (x-µ)/σ
= (55-50)/10
= 5/10
=1/2
=0.50
Therefore z score for x=55 is 0.50
. For the given normal distribution, µ=50 and σ=10.
2) The z score for x=35 is computed as follows:
Z= (x-µ)/σ
= (35-50)/10
= -15/10
=-3/2
=-1.50
Therefore z score for x=55 is -1.50