Erik and Nita are playing a game with numbers. In the game, they each think of a random number from zero to 20. If the difference between their two numbers is less than 10, then Erik wins. If the difference between their two numbers to greater than 10, then Nita wins. Use what you know about inequalities and absolute values to better understand the game. 1. a) Which player did you select?
1. b) What number did the other player pick?
2. Should you use an equation or an inequality to represent the ways your player can win. Explain why.
3. If Erik had a 4 and Nita had a 12, would the winner be different if Nita got the 4 and Erik got the 12?
4. Is it appropriate to use an absolute value function to represent how people win this game? Why?
5. If your player is Erik, write an expression that shows all of the ways that Erik will if Nita chooses 7. If your player is Nita, write an expression that shows all of the ways that Nita will win if Erik chooses 17 (be sure to define your variables)
6. In order to graph your solution, solve for the variable. Be sure to show your work.
7. Sketch a graph of your solution.
8. What is the range of numbers that will win the game for your player. If your player is Erik, assume that Nita chooses 7. If your player is Nita, assume that Erik chooses 17.
9. Graph all the possible numbers that your player could pick. Compare this graph to your answer in question 8. If your player is Erik, and Nita chooses 7, does Erik have a good chance of winning? If your player is Nita, and Erik chooses 17, does Nita have a good chance of winning?

Jobs and productivity! how do retail stores rate? one way to answer this question is to examine annual profits per employee. the following data give annual profits per employee (in units of 1 thousand dollars per employee) for companies in retail sales. assume σ ≈ 4.0 thousand dollars. 3.7 6.7 3.6 8.5 7.5 5.9 8.7 6.4 2.6 2.9 8.1 −1.9 11.9 8.2 6.4 4.7 5.5 4.8 3.0 4.3 −6.0 1.5 2.9 4.8 −1.7 9.4 5.5 5.8 4.7 6.2 15.0 4.1 3.7 5.1 4.2 (a) use a calculator or appropriate computer software to find x for the preceding data. (round your answer to two decimal places.) thousand dollars per employee (b) let us say that the preceding data are representative of the entire sector of retail sales companies. find an 80% confidence interval for μ, the average annual profit per employee for retail sales. (round your answers to two decimal places.) lower limit -- thousand dollars upper limit -- thousand dollars (c) let us say that you are the manager of a retail store with a large number of employees. suppose the annual profits are less than 3 thousand dollars per employee. do you think this might be low compared with other retail stores? explain by referring to the confidence interval you computed in part (b). yes. this confidence interval suggests that the profits per employee are less than those of other retail stores. no. this confidence interval suggests that the profits per employee do not differ from those of other retail stores. correct: your answer is correct. (d) suppose the annual profits are more than 6.5 thousand dollars per employee. as store manager, would you feel somewhat better? explain by referring to the confidence interval you computed in part (b). yes. this confidence interval suggests that the profits per employee are greater than those of other retail stores. no. this confidence interval suggests that the profits per employee do not differ from those of other retail stores. (e) find an 95% confidence interval for μ, the average annual profit per employee for retail sales. (round your answers to two decimal places.) lower limit 3.75 incorrect: your answer is incorrect. thousand dollars upper limit 6.41 incorrect: your answer is incorrect. thousand dollars