Answer
P(x̄ > 83) = 0.0668. It implies that out of 100 samples, about 7 samples will have mean > 83.
Work Step by Step
To calculate P(x̄ > 83), we need to find the a-score:
$z = \frac{x̄ - μ_{x̄}}{σ_{x̄}}$
$= \frac{83-80}{2}$ = 1.5
P(z > 1.5) = 0.0668, hence:
P(x̄ > 83) = 0.0668