A college student recently purchased a multiplayer video game. Before playing, the college student looked up statistics on how fast gamers were completing the full playthrough of the game. Of the 500 players that have completed the game, 331 of them completed the full game in less than 49 minutes. Use Excel to determine the probability that in a sample of 45 games, 30 or fewer of them were completed in less than 49 minutes. Round your answers to two decimal places.

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.