Answer
0.0040
Work Step by Step
Here we have n = 20, hence:
$σ_{x̄} = σ / \sqrt n = 16 / \sqrt 50 = 2.26$
To calculate $P(x̄ \leq 260)$, we need to find the z-score:
$z = \frac{x̄ - μ_{x̄}}{σ_{x̄}}$
$= \frac{260-266}{2.26}$ = -2.65
P(z \leq -2.65) = 0.0040, hence:
$P(x̄ \leq 260) = 0.0040$
