2. Full-time Ph. D. students receive an average salary of $12,837 according to the US Department of Education. The dean of graduate studies
at a large university claims that
Ph. D. students in his state earn more than this. He surveys 44 randomly selected
students and finds their average salary is $14.445 with a standard deviation of $1500
With a = 0.01, is the dean's claim correct?

Our star pitcher, foster enlight, can throw a pitch so fast that it gets to the catcher’s mitt before it leaves foster’s fingers! if the team wins a game then the probability that foster was pitching is 0.8 but only if foster had at least one day’s rest since his last pitching assignment. if foster does not have a day off and the team still wins, the probability that foster was pitching drops by half of what it was on the previous day. if the team wins three games in succession from the toronto tachyons and foster pitched in game #2, what is the probability that he pitched in one or more of the other games? (assume that foster did not pitch on the day before the first game of this three game series.)