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?

The mean salary of the junior executives is $28890.8                  

Step-by-step 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:

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:

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

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