Answer
0.0011
Work Step by Step
Here n=12.
$σ_{x̄} = σ / \sqrt n= 4.2 / \sqrt 12 = 1.21$
To calculate P(x̄ < 40), we need to find the z-score:
$z = \frac{x̄ - μ_{x̄}}{σ_{x̄}}$
$= \frac{40-43.7}{1.21}$ = -3.06
P(z < -3.06) = 0.0011, hence:
P(x̄ < 40) = 0.0011
