5.2a z-Score of a Normal Distribution


5.2a z–Score of a Normal Distribution
 
Example:
(a)  A normal distribution has a mean, µ = 50 and a standard deviation σ = 10. Calculate the standard score of the value X = 35.
(b)  The masses of Form 5 students of a school are normally distributed with a mean of 60 kg and a standard deviation of 15 kg.
Find
(i) the standard score of the mass of 65 kg,
(ii) the mass of a student that corresponds to the standard score of – ½.

Solution:
(a)
X ~ N (µσ2).
X ~ N (50, 102)
Z = X μ σ = 35 50 10 = 1.5

(b)(i)
X – Mass of a Form 5 student
X ~ N (µσ2).
X ~ N (60, 152)
Z = X μ σ = 65 60 15 = 1 3
Hence, the standard score of the mass of 65 kg is .

(b)(ii)
Z = – ½,
Z = X μ σ 1 2 = X 60 15 X 60 = 1 2 ( 15 ) X = 52.5

Hence, the mass of a Form 5 student that corresponds to the standard score of –
½ is 52.5 kg.

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