The probability that a worker selected at random makes between $ 300 and $ 350 is 0.1359 .
Step-by-step explanation:
We have , Weekly wages at a certain factory are normally distributed with a mean of $400 and a standard deviation of $ 50.
Step 1: Sketch the curve.
The probability that 300<X<350 is equal to the blue area under the curve.
Step 2:
Since μ=400 and σ=50 we have:
P ( 300<X<350 )=P ( 300−400< X−μ<350−400 )
⇒ P ( (300−400)/50 < (X−μ)/σ < (350−400)/50)
Since Z=(x−μ)/σ , (300−400)/50=−2 and (350−400)/50=−1 we have:
P ( 300<X<350 )=P ( −2<Z<−1 )
Step 3: Use the standard normal table to conclude that:
P ( −2<Z<−1 )=0.1359
