Answer
P(x̄ > 46) = 0.0166. This result is unusual as the probability is less than 0.05.
Work Step by Step
Here n=12.
$σ_{x̄} = σ / \sqrt n= 4.2 / \sqrt 15 = 1.081$
To calculate P(x̄ > 46), we need to find the z-score:
$z = \frac{x̄ - μ_{x̄}}{σ_{x̄}}$
$= \frac{46-43.7}{1.08}$ = 2.13
P(z > 2.13) = 0.0166, hence:
P(x̄ > 46) = 0.0166
