Answer
P(x̄ > 95) = 0.0418
Work Step by Step
$σ_{x̄} = σ / \sqrt n = 10/\sqrt 12 = 2.87$
To calculate P(x̄ > 95), we need to find the z-score:
$z = \frac{x̄ - μ_{x̄}}{σ_{x̄}}$
$= \frac{95-90}{2.87} = 1.73 $
P(z > 1.73) = 0.0418, hence:
P(x̄ > 95) = 0.0418
