Answer
0.9845
Work Step by Step
$σ_{x̄} = σ / \sqrt n = 16 / \sqrt 15 = 4.13$
To calculate $P(256 \leq x̄ \leq 276)$, we need to find the z-score:
$z = \frac{x̄ - μ_{x̄}}{σ_{x̄}}$
$= \frac{256-266}{4.13} = -2.42 $
$= \frac{276-266}{4.13} = 2.42 $
$P(-2.42 \leq z \leq 2.42) = 0.9845$, hence:
$P(256 \leq x̄ \leq 276) = 0.9845$
