Let x be the normal variable denoting the annual salaries of employees
a) Probability of people earning less than $40,000 is given by:
[tex]P(x<40000)=P(z<\frac{40000-50000}{20000})[/tex]
then:
[tex]=P(z<\frac{-10000}{20000})=P(z<\frac{-1}{2})=P(z<-0.5)[/tex]
From z tables
[tex]=0.3085[/tex]
Thus, in percent 0.3085 x 100 = 30.85%
Answer: People earn less than $40,000 is 30.85%
Graph
b) Probability of people earning between $40,000 and $70,000 is:
[tex]P(40000Then[tex]\begin{gathered} =P(\frac{-10000}{20000}From z tables[tex]=0.8413-0.3085=0.5328[/tex]
This is in percent 0.5328 x 100 = 53.28%
Answer: 53.28% of people earn between $40,0000 and $70,000
Graph
c) Probability of people earning more than $70,000 is:
[tex]P(x>70000)=1-P(z<\frac{70000-50000}{20000})[/tex]
Then
[tex]=1-P(z<\frac{20000}{20000})=1-P(z<1)[/tex]
From z tables
[tex]=1-0.8413=0.1587[/tex]
In percent is 0.1587 x 100 = 15.87%
Answer: The percent of people who earn more than $70,000 is 15.87%
Graph
