Afarmer has 70 lbs of apples and 90 lbs of potatoes for sale. the market price for apples (per pound) each day is a random variable with a mean of 0.9 dollars and a standard deviation of 0.2 dollars. similarly, for a pound of potatoes, the mean price is 0.4 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 tarmer's net income o a. a pounds of apples sold, p number of ib of potatoes sold, profit 0.5a+0.4p ○ c. asprice per pound or apples, p = price per pound of potatoes. profit 70a +90p-5 o b. a pounds of apples sold, p number of lb of potatoes sold, profit 0.5a+0.4p - 5 o d-as price per pound of apples, p = price per pound of potatoes. prott-70a + 90p b) find the mean. the mean profit isdollars. c) flnd the standard devlation of the net income. the standard deviation is dollars. (round to two decimal places as needed.) d) do you need to make any assumptions in calculating the mean? a. yes; the variables must be discrete. o b. yes; the o c. yes; the prices must be dependent. prices must be independent. d. no; no assumptions are made in calculating the mean. do you need to make any assumptions in calculating the standard deviation? a. yes; the variables must be discrete. o b. yes; the prices must be dependent. o c. yes; the prices must be independent. 0 d. no: no assumptions are made in calculating the standard deviation