Answer
0.0071
Work Step by Step
Here n = 24
$σ_{x̄} = σ / \sqrt n = 10/\sqrt 24 = 2.04$
To calculate P(x̄ > 95), we need to find the z-score:
$z = \frac{x̄ - μ_{x̄}}{σ_{x̄}}$
$= \frac{95-90}{2.04} = 2.45 $
P(z > 2.45) = 0.0071, hence:
P(x̄ > 95) = 0.0071
