Definition: - The units marked on the horizontal axis of the standard normal curve are obtained by z and are called the z score or z value. A specific value of z gives the distance between the mean and the point represented by z in terms of standard deviation.
Note: - The values on the right side of the mean are positive and those on the left side are negative.
The z score for a point on the horizontal axis gives the distance between the mean and the point represented by z in terms of the standard deviation.
Z score formula: - For a normal random variable x, a particular value of x can be converted to its corresponding z value by using the formula
Z= (x- µ)/σ
Where µ and σ are the mean and standard deviation of the normal distribution of x, respectively.
Example: - Let x be a random variable with its mean equal to 40 and standard deviation equal to 5. Find the z score for
1) X=49
2) X= 55
Solution: - According to the problem the population mean and standard deviations are 40 and 5 respectively.
Hence µ= 40 and σ=5.
1) For x= 49,
z score =(x-µ)/σ
=(49 – 40) / 5
= 1.80
Therefor z score for x= 49 is 1.80
2) For x= 55
z score =(x-µ)/σ
= (55-40) / 5
= 3.00
Therefor z score for x= 55 is 3.00