Question

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 . Help

Answer 1

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