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?

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ChiKesselman ChiKesselman · Answer 1 · 2020-04-13T05:26:53+02:00

Answer:

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:

[tex]z_{score} = \displaystyle\frac{x-\mu}{\sigma}[/tex]

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:

[tex]P( X < 28000) = P( z < \displaystyle\frac{28000 - \mu}{1700})=0.3[/tex]

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

[tex]\displaystyle\frac{28000 - \mu}{1700}= -0.524\\\\\mu=28890.8[/tex]

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