Hadey the goat and Taylor the tailor are preparing to launch their new clothing line collab "Commes des Mouflons". The preorders for the jackets are already rolling in, with the number of orders each day "X" having the distribution shown below. Assume that the number of orders each day is an independent variable.

X P(X=x) 0 0.6 1 0.3 2 0.04 3 0.03 4 0.02 5 0.01

Questions:

a. Describe the shape of the distribution of daily jacket orders. b. How many jacket orders should Taylor and Hadey EXPECT each day? c. What is the standard deviation of the number of daily jacket orders? d. How many jacket orders should Taylor and Hadey EXPECT each week? e. What is the standard deviation in the TOTAL number of jacket orders per WEEK?

f. If the pre-order price for a jacket is $240, how much revenue should Hadey and Taylor EXPECT in the month of May? g. If each jacket takes Taylor 3 hours to produce, how much time should she EXPECT to devote to production for the month of May? h. What is the standard ERROR in the number of jacket orders per day in the month of May? i. What shape does the distribution of the mean orders PER DAY in the month of May look like? j. Taylor doesn't want to give up her existing business, so she's looking to hire an assistant to help with the jackets. Hadey says that they can't afford that unless they bring in more than $4000 from pre-orders in May. Recall that the pre-order price is $240 per jacket. How many TOTAL pre-orders would they need in May to meet this goal? k. In order to meet the number of orders you found in part j, how many jacket pre-orders would need to come in PER DAY in the month of May? l. Using your calculations from parts j and k, what is the probability that Hadey and Taylor will get enough jacket pre-orders in the month of May to afford to hire an assistant?