Answer
P(x̄ > 2.55) = 0.0778
This result is not unusual so it does not contradict with the results in part (b)
Work Step by Step
$σ_{x̄} = 1.38 / \sqrt 40 = 0.218$
To calculate P(x̄ > 2.55), we need to find the z-score:
$z = \frac{x̄ - μ_{x̄}}{σ_{x̄}}$
$= \frac{2.55 - 2.24}{0.218}$ = 1.42
P(z > 1.4) = 0.0778, hence:
P(x̄ > 2.55) = 0.0778
