Answer
$P(78.3 \leq x̄ \leq 85.1) = 0.797$
Work Step by Step
To calculate P(x̄ > 78.3), we need to find the z-score:
$z = \frac{x̄ - μ_{x̄}}{σ_{x̄}}$
$= \frac{78.3-80}{2}$ = -0.85
To calculate P(x̄ < 85.1), we need to find the z-score:
$z = \frac{x̄ - μ_{x̄}}{σ_{x̄}}$
$= \frac{85.1-80}{2}$ = 2.55
Using technology (or Table V), we have:
$P(-0.85 < Z < 2.55) = 0.797$ , hence:
$P(78.3 \leq x̄ \leq 85.1) = 0.797$
