Mr. smith owns two appliance stores. in store a the number of tv sets sold by a salesperson is, on average, 13 per week with a standard deviation of 5. in store b the number of tv sets sold by a salesperson is, on average, 7 with a standard deviation of 4. mr. smith has a position open for a person to sell tv sets. there are two applicants. mr. smith asks one of them to work in store a and the other in store b, each for one week. the salesperson in store a sold 10 sets, and the salesperson in store b sold 6 sets.

mr. smith realizes that store a typically has more customers and typically sells more tvs than store b, so it would not be fair to simply compare the raw data. what he needs to do is "level the playing field" by comparing the two after adjusting for the differences between the two stores.

(a) based on this information, which person should mr. smith hire?

(b) suppose the person not hired asks mr. smith "well, how many would i have had to sell to be exactly as good as the person you hired? " what should mr. smith say? (not quite realistic, because the answer may not be an integer, but just give the floating point value.)

hint: use standardized random varibles.