For a given set of data, the standard score, \(z\), corresponding to the raw score, \(x\), is given by \(z=\dfrac{x-\mu}{\sigma}\), where \(\mu\) is the mean of the set and \(\sigma\) is the standard deviation. If, for a set of scores, \(\mu=78\) and \(\sigma = 6\), which of the following is the raw score, \(x\), corresponding to \(z=2\) ?

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We can simply substitute values into the equation.

$$ z=\frac{x-\mu}{\sigma} $$ $$ 2=\frac{x-78}{6} $$ $$ 12 = x-78 $$ $$ x = \boxed{90} $$