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A farmer has 120lbs of apples and 50lbs of potatoes for sale. The market price for apples​ (per pound) each day is a random variable with a mean of 0.8 dollars and a standard deviation of 0.3dollars.​ Similarly, for a pound of​ potatoes, the mean price is 0.3 dollars and the standard deviation is 0.1 dollars. It also costs him 3 dollars to bring all the apples and potatoes to the market. The market is busy with​ shoppers, so assume that​ he'll be able to sell all of each type of produce at that​ day's price. Complete parts​ a) through​ d). Make sure to consider all necessary assumptions before calculating. 

a. Define your random​ variables, and use them to express the​ farmer's net income.

A = sprice per pound of​ apples,  P  =  price per pound of potatoes,  Profit equals 120A plus 50P minus 3

Find the mean:

120*0.8 + 50*0.3 - 3 = 108

The standard deviation 

= sqrt(120^2 * 0.3^2 + 50^2 * 0.1^2)  = 35.35

No; no assumptions are made in calculating the mean.

The Assumption of independence is needed when calculating the standard deviation. 

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