You are in sales. you only sell one item, you are the only salesperson at the store, and people never buy more than one unit of your item. suppose there is a new test to predict if a person who randomly walks into the store is going to buy the item. the test occurs right as the person walks into the store. the test returns positive if it predicts that the person is going to buy the item. we know that only 10% of people buy the item. when someone does buy the item, the test returns the result that the person will buy the item 90% of the time. when someone doesn't buy the item, the test returns the result that the person will buy the item 20% of the time. you make $1,000 from each sale. this is your only salary from the store. a) what is your expected take home salary each week assuming an average of 20 random people walk into the store each week? b) you are thinking of using the test to your advantage and want to try one week where you only try to sell to people who test positive for the test. what is your new expected take home salary each week? c) how many people do you expect to talk with each week, on average, in this new regime where you only talk with people who test positive? round your answer to one decimal place. d) what is the probability that a person who enters the store is going to buy something given that they have a positive test result? round your answer to two decimal places. e) what is the probability that a person who enters the store is going to buy something given that they have a negative test result? round your answer to four decimal places.