The annual salaries of employees in a large company are appr

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.

a. What percent of people earn less than $40,000?

b. What percent of people earn between $45,000 and $65,000?

c. What percent of people earn more than $70,000?

Solution

Mean ( u ) =50000
Standard Deviation ( sd )=20000
Normal Distribution = Z= X- u / sd ~ N(0,1)                  
a)
P(X < 40000) = (40000-50000)/20000
= -10000/20000= -0.5
= P ( Z <-0.5) From Standard Normal Table
= 0.3085                  
b)
To find P(a < = Z < = b) = F(b) - F(a)
P(X < 45000) = (45000-50000)/20000
= -5000/20000 = -0.25
= P ( Z <-0.25) From Standard Normal Table
= 0.40129
P(X < 65000) = (65000-50000)/20000
= 15000/20000 = 0.75
= P ( Z <0.75) From Standard Normal Table
= 0.77337
P(45000 < X < 65000) = 0.77337-0.40129 = 0.3721  
c)
P(X > 70000) = (70000-50000)/20000
= 20000/20000 = 1
= P ( Z >1) From Standard Normal Table
= 0.1587