The score that is one and a half standard deviation is 182.
The z score is used to determine by how many standard deviations the raw score is above or below the mean. It is given by:
[tex]z=\frac{x-\mu}{\sigma} \\\\where\ x\ is\ raw\ score, \mu\ is\ mean, \sigma\ is\ standard \ deviation[/tex]
Given that:
μ = 140, σ = 28. For a z score of 1.5(one and a half):
[tex]1.5=\frac{x-140}{28} \\\\x-140=42\\\\x = 182[/tex]
The score that is one and a half standard deviation is 182.
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