Answer
$P(\bar{x} < 24.3) = 0.9726$
It is not unusual for the mean to be less than 24.3
Work Step by Step
n = 64
$\sigma$ = 1.25
$\mu$ =24
Want to find P($\bar{x}$ < 24.3):
i) Find the z score corresponding to 24.3
z = $\frac{\bar{x} - \mu}{\frac{\sigma}{\sqrt n}}$
z = $\frac{24.3 - 24}{\frac{1.25}{\sqrt 64}}$
z = 1.92
ii) $P( z < 1.92) = 0.9726$
iii) Therefore $P(\bar{x} < 24.3) = 0.9726$
It is not unusual for the mean to be less than 24.3. We can infer this because the corresponding z-score is less than 2.