Question

A professional language translator gets paid an average of $320 per hour with a standard deviation of $41.75 per hour. What proportion of professional language translators get paid less than $250 per hour? Assume the population is normally distributed. Round your answer to four decimal places

Answer 1

0.0475 or 4% professional language translators get paid less than $250 per hour

Explanation:

Mean = 320

Standard Deviation = 41.75

We need to find proportion of professional language translators get paid less than $250 per hour i.e P(x<250)

First we will find value of z

Using formula:
`z=(x-\mu)/(\sigma)`

We have x=250, finding z

`z=(x-\mu)/(\sigma)\\z=(250-320)/(41.75)\\z=-1.67`

Now we will find P(z<-1.67) by looking into the normal distribution table

`P(z<-1.67)=0.0475\\`

So,0.0475 or 4% professional language translators get paid less than $250 per hour