Question

The annual salaries of employees in a large company are approximately normally distributed with a mean of $50,000$ and a standard deviation of $20,000$. What percent of people earn between $45,000$ and $65,000$?

• A. $56.23$%
• B. $47.4$%
• C. $37.2$%
• D. $38.56$%

Answer 1

Answer: (C)

$37.2$%

Let $x$ be the annual salary of employees in a large company.
$x$ has $\mu =50000,\sigma =20000$.
We know that for given $x,z=\frac{x-\mu }{\sigma }$
We have to find the percent of people earning between $45,000$ and $65,000$
First let us find $P(45000<x<65000)$
For $x=45000,z=\frac{45000-50000}{20000}=-0.25$
and for $x=65000,z=\frac{65000-50000}{20000}=0.75$
$\therefore P(45000<x<65000)=P(-0.25<z<0.75)$
$=P(z<0.75)-P(z<-0.25)$
$=0.7734-(1-0.5986)$ (from normal distribution table)
$=0.372$
$\therefore P(45000<x<65000)=0.372=37.2\%$
Hence the percent of people earning between $45,000$ and $65,000$ is $37.2\%$