Weekly wages at a certain factory are normally distributed with a mean of
$400 and a standard deviation of $50.
Find the probability that a worker
selected at random makes between
$400 and $450.

We must use the formula of the z-score to find the the probability that a worker selected at random makes between $400 and $450 dollars. Then let X1 = 400 and X2 = 450 with the mean μ = 400 and standard deviation σ = $50. Then,

z1 = (X1 - μ) / σ = (400-400) / 50 = (0/50) = 0.00 and

z2 = (X2 - μ) / σ = (450 - 400) / 50 = (50/50) = 1.00

Then, the probability yields, P(0.00 ≤ z ≤ 1.00) = 0.3413 - 0.0000 = 0.3413