[tex]\begin{gathered} \text{ Using the formula Z=}\frac{x-\mu}{\sigma} \\ \text{Where Z= s}\tan dard\text{ score, }\mu=sample\text{ mean, }\sigma=\text{ sample standard deviation} \\ From\text{ the question, } \\ z=2.5,\text{ }\mu=97,\text{ }\sigma=12, \\ \text{substituting theses values into the equation above, we have} \\ 2.5=\frac{x-97}{12} \\ 2.5\text{ x 12 = x-97} \\ 30=x-97 \\ x=30\text{ + 97} \\ x=127 \end{gathered}[/tex]
The value that is 2.5 standard deviations above the mean is 127
