Answer to Question #125026 in Statistics and Probability for Igor Valkama

Question

In Company XYZ, the monthly salaries of all employees are normally distributed with a mean of 5 000€ and a standard deviation of 1 200€. What is the level of salary that 20% of the company's employees earn less than?

Answer 1

Given :

x is the random variable of salary

Mean= 5000

sd=1200

P(X<x)=0.20

solution :

Step 1: find Z score for given 20%(0.20)

Using Z table or invnorm(0.20) on ti84 , we get z=-0.85 for area = 0.20.

Step 2: now we use Z score formula , mean and sd given to find x

Using Z= (x-mean)/sd

-0.85 = (x-5000)/1200

-1020=x-5000

Hence x= 5000-1020

X= 3980

Hence the $3980 is the level of salary that 20% of the company's emploees can less than.