Question

Suppose toyota manufacturing plant employs a total of 100 workers and pays a mean monthly salary of $ 5,000 to the employees in the organization. The mean monthly salary paid to male and female employees are $ 5,200.00 and $ 4,200 respectively. Determine the number of males and females employed by the organization.

Answer 1

Answer: The number of males in the organization is 80 while the number of females is 20.

We follow the steps below to arrive at the answer.

Let 'x' be the proportion of male employees.

Then number of female employees will be $\mathbf{1-x}$

We can rewrite the average monthly salary as the total of products of proportion of males and females in the sample and their respective salaries.

Mathematically this is represented as follows:

$\mathbf{5000 = 5200x + (1-x)*4200}$

Solving for x we get,

$5000 - 4200 = 5200x -4200x$

$800 = 1000x$

$\mathbf{x = \frac{800}{1000}= 0.8}$

Since there are 100 employees, we arrive at the number of males by multiplying the proportion of males and total number of employees.

$\mathbf{0.8 * 100 =80}$

So, number of females is $\mathbf{100 -80 =20}$