Think of all of the different games that have been presented in this lesson: rolling a die, using a spinner, drawing a card from a deck, etc. Sometimes the results ended favorably for one person over another, but that’s not what we want for this activity. Can you design a fair game? Use this worksheet to design a game whose expected value is 0. Be sure to define the rules of play. Prove that your game is fair using the expected value calculation. PLZZZ HEL ASAP

An automobile assembly line operation has a scheduled mean completion time, μ, of 12 minutes. the standard deviation of completion times is 1.6 minutes. it is claimed that, under new management, the mean completion time has decreased. to test this claim, a random sample of 33 completion times under new management was taken. the sample had a mean of 11.2 minutes. assume that the population is normally distributed. can we support, at the 0.05 level of significance, the claim that the mean completion time has decreased under new management? assume that the standard deviation of completion times has not changed.