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.

Answer 1

Since 400 is the mean and the standard deviation is 50, $400-$450 is +1 standard deviation. One standard deviation is 34.1% probability that the worker's wages would fall in this range.

The graph is for different data but is the same concept.

https://commons.wikimedia.org/wiki/User:Cmglee/svg#/media/File:Standard_deviation_diagram_US_men_heights.svg

Answer 2

Greetings! Lets solve this shall we ?

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

I hope this helped!