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

Answer:

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

Step-by-step 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: $z=\frac{x-\mu}{\sigma}$

We have x=250, finding z

$z=\frac{x-\mu}{\sigma}\\z=\frac{250-320}{41.75}\\z=-1.67$

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