Z Score Example

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


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