For the question below I am stuck with part E. The standard deviation of estimated profit z=2000x+3500y

Gain Communications sells aircraft communication units to both military and the civilian markets. Next year's sales depend on market conditions that cannot be predicted exactly. Gain follows the modern practice of using probability estimates of sales. The military division estimates its sales as follows:

Units sold10003000500010,000

Probability0.10.3.4.2

These are personal probabilities that express the informed opinion of Gain's executives. The corresponding sales estimates for the civilian division are

Units sold300500750

Probability0.40.50.1

Take X to be the number of military units sold and Y the number of civilian units sold.

a)From the probability distribution compute the estimated average sales for military division and civilian division.

Probability distribution estimated average sales for Military division _x= 5000 and the probability distribution estimated average sales for civilian division _y= 445

= 5000

= 445

b)Gain makes a profit of $2000 on each military unit sold and $3500 on each Civilian unit. Calculate next year's total profit for gain Communication.

Gain communication total profit next year $11,557,500

= 11557500

c)Find the variance and standard deviation of military sales(X) and civilian sales(Y).

Variance of military sales(x) is 7,800,000

Standard deviation of military sales(x) 279.85

Variance of civilian sales(y) is 19,225

Standard deviation of civilian sales(y) is 138.65

= 7,800,000

= 2792.848

=19,225

= 138.654

d)Because the military budget and the civilian economy are not closely linked, Gain is willing to assume its military and civilian sales vary independently. What is the standard deviation of Gain's total sales(X+Y)?

The standard deviation of Gain's total sales 2796.29

= 7819225

= 2796.28771

e)Find the standard deviation of estimated profit (Z = 2000X+3500Y).