Need help with 10-13.

Question 6 5 pts Ponchos Instructions: Use at least 4 decimals in your calculations (unless the calculated number's decimals do not go out that far). Then round your answer to the requested number of decimals. Ana is an entrepreneur in a developing country who produces ponchos in a sewing room in her home. (She is part of the "informal" manufacturing sector.) The number of ponchos Ana produces per day is a random variable X, which has the probability distribution given below. Numbers of ponchos produced on different days are independent. 39 40 41 42 Px(x) 0.3 0.4 0.2 0.1 This is the first of 13 questions in this set. Calculate the probability Ana will produce more than 40 ponchos on any one day. One decimal Question 7 5 pts Calculate the expected number of ponchos Ana produces in a day. One decimal Question 8 5 pts Calculate the variance of the number of ponchos produced in a day. Two decimals Question 9 5 pts Calculate the probability that, in a period of five days, Ana will produce more than 40 ponchos on at least one day. Four decimals HINT: You can answer this question, and the next one, using the binomial probability function, but that is not necessary.Question 10 5 pts Calculate the probability that Ana will produce more than 40 ponchos on all five days. Four decimals Question 11 5 pts The production cost of a poncho (in dollars) is Y = 2 + 24(1/X). Calculate expected cost per poncho. Four decimals HINT: Begin by specifying the probability distribution of Y (the different possible values of Y, and the probability that each will occur). Alternatively, you can specify the probability distribution of 1/X, and then use the results we have about the mean and (in the next question) variance of a linear transformation. (Y is not a linear transformation of X, but Y is a linear transformation of 1/X.) Question 12 5 pts Calculate the variance of cost per poncho. HINT: Keep more than 4 decimals when you do the calculation, because the answer is a small number. Four decimals Question 13 5 pts Revenue per poncho (in dollars) is R = 12 - 0.1X. (This revenue function reflects the fact that Ana must cut the price in order to sell more.) Calculate expected revenue per poncho. HINT: Use our results about the mean and (in the next question) variance of a linear transformation. Two decimals