The method for computing a z-score is [tex]\bold{z = \frac{(x-\mu)}{\sigma}}[/tex], where x is the crude score, [tex]\bold{\mu}[/tex] is the mean population, and [tex]\bold{\sigma}[/tex] seems to be the standard population difference.
[tex]\bold{\bar{x}=150}\\\\ \bold{\sigma=25}[/tex]
following are the calculation of the Z scores:
[tex]\to \ (a)\ 100:\ \text{Z score}=\frac{(100-150)}{25}= \frac{(-50)}{25} = -2\\\\\to \ (b)\ 120:\ \text{Z score}=\frac{(120-150)}{25}= \frac{(-30)}{25} = -1.2\\\\\to \ (c)\ 140:\ \text{Z score}=\frac{(140-150)}{25}= \frac{(-10)}{25} = -0.4\\\\\to \ (a)\ 160:\ \text{Z score}=\frac{(160-150)}{25}= \frac{(10)}{25} = 0.4\\\\[/tex]
Using formula:
[tex]\to \text{Raw score = Mean(series) +Z score} \times \text{SD(series)}[/tex]
Calculating the Raw scores:
[tex]\text{(e) -1: Raw score= 150 +(-1)} \times 25 = 125 \\\\\text{(f) -0.8: Raw score= 150 +(-0.8)} \times 25 = 130\\\\\text{(e) -0.2: Raw score= 150 +(-0.2)} \times 25 = 145\\\\\text{(e) 1.38: Raw score= 150 +(1.38)} \times 25 = 184.5\\\\[/tex]
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