Question

2. The income of junior executives in a large corporation are normally distributed with a standard deviation of $1700. A cutback is pending, at which time those who earn less than $28,000 will be discharged. If such a cut represents 30% of the junior executives, what is the current mean (average) salary of the group of junior executives?

Answer 1

The mean salary of the junior executives is $28890.8

Explanation:

We are given the following in the question:

Standard Deviation, σ = $1700

We are given that the distribution of income of junior executives is a bell shaped distribution that is a normal distribution.

Formula:

`z_(score) = \displaystyle(x-\mu)/(\sigma)`

30% of the junior executives earn less than $28,000. We have to find the mean salary of the junior executives.

Thus, we can write:

`P( X < 28000) = P( z < \displaystyle(28000 - \mu)/(1700))=0.3`

Calculation the value from standard normal z table, we have,

`\displaystyle(28000 - \mu)/(1700)= -0.524\\\\\mu=28890.8`

Thus, the mean salary of the junior executives is $28890.8