Question

3. A graduate student believes that his starting salary will be based on his thesis professors salary, in the form of the equation Y 400000.60 (X -10000) where Y is the students average salary and X is the thesis professors salary. Consider a population of 100 graduate students, with an average thesis professor salary of $125,000 and standard deviation $30000 (a) Find the expected student salary based on this equation (b) Find and interpret the standard deviation of student salary.

Answer 1

(a)

The given equation is written as follows:

i.e.,

(1)

By Theorem:

(2)

Applying (2), equation (1) becomes:

(3)

Given:
E(X)=125000 (4)

Substituting (4), equation (3) becomes:

So,

Answer is:

109000

(b)

By Theorem:

(5)

Given:

(6)

Substituting (6), equation (5) becomes:

So,

Answer is:

324,000,000

(c)

Standard deviation of Y is given by:

(200,000 - 109,000)/18,000 = 5.0556

It would be unusual to see a student salary of $200,000 because 200,000 is 5.0556 > 2 standard deviations away from the average.