Question

PLEASE HELP 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 betweenh
$250 and $300.

Answer 1

Answer: 0.0215 .

Explanation:

Let X denotes the weekly wages at a certain factory .

It is normally distributed , such that

`X\sim N(\mu=400,\ \sigma= 50)`

Then, the probability that a worker selected at random makes between

$250 and $300:

`P(250<X<300)=P((250-400)/(50)<(x-\mu)/(\sigma)<(300-400)/(50))\\\\=P((-150)/(50)<z<(-100)/(50))\ \ [z=(x-\mu)/(\sigma)]\\\\=P(-3<z<-2)\\\\=P(z<-2)-P(z<-3)\\\\=1-P(z<2)-(1-P(z<3))\\\\=P(z<3)-P(z<2)\\\\=0.9987-0.9772\\\\=0.0215`

Hence,the required probability = 0.0215 .