Answer
The probability is not unusual. Since the probability is not high, the new program is not any more effective than the previous program.
Work Step by Step
Here n = 20
$σ_{x̄} = σ / \sqrt n = 10/\sqrt 20 = 2.24$
To calculate $P(x̄ \geq 92.8)$, we need to find the z-score:
$z = \frac{x̄ - μ_{x̄}}{σ_{x̄}}$
$= \frac{92.8-90}{2.24} = 1.25 $
P(z > 1.25) = 0.1056, hence:
$P(x̄ \geq 92.8) = 0.1056$
