Answer
0.0041
Work Step by Step
Here n=9.
$σ_{x̄} = σ / \sqrt n= 4.2 / \sqrt 3 = 1.4$
To calculate P(x̄ < 40), we need to find the z-score:
$z = \frac{x̄ - μ}{σ}$
$= \frac{40-43.7}{1.4}$ = -2.64
P(z < -2.64) = 0.0041, hence:
P(x̄ < 40) = 0.0041
