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 $300 and $350.

Question

I need to the percentage.

Answer 1

let x = wages

x is normally distributed with mean 400 and standard deviation (SD) 50

z = (x - mean)/SD is N(0,1). For our problem z = (x - 400)/50

want to find P(300 < x < 350)

translate limits of above from x to z using formula for z:

P(300 < x < 350) = P( (300-400)/50 < z <M (350-400)/50) = P(-2 < z < -1) = P(z < -1) - P(z < -2) = 0.1587 - 0.0228 = 0.1359.