Answer
$P(0.260 \leq p̂ \geq 0.300) = 0.6827$. Hence it will not be unusual as the probability is quite high.
Work Step by Step
To calculate $P(0.260 \leq p̂ \geq 0.300)$, we need to find the z-score:
$z = \frac{p̂ - μ_{p̂}}{σ_{p̂}}$
$= \frac{.260-.280}{0.02}$ = -1.0
$= \frac{.300-.280}{0.02}$ = 1.0
$P(-1.0 z \geq 1.0) = 0.6827$, hence:
$P(0.260 \leq p̂ \geq 0.300) = 0.6827$ (not unusual)
