Answer
$P(x̄ \leq 75.8) = 0.0179$. It means out of 100 samples about 2 samples will have a mean less than 75.8
Work Step by Step
To calculate $P(x̄ \leq 75.8)$, we need to find the z-score:
$z = \frac{x̄ - μ_{x̄}}{σ_{x̄}}$
$= \frac{75.8 - 80}{2}$ = -2.1
$P(z \leq -2.1) = 0.0179$, hence:
$P(x̄ \leq 75.8) = 0.0179$
