The average speed of a volleyball serve is 57 miles per hour. Natalie practiced a new technique to improve her serving speed. Her coach recorded the speed of 36 random serves during practice and found that her average speed using the new technique was 58.9 miles per hour, with a standard deviation of 2.8 miles per hour.

Part A: State the correct hypotheses if Natalie is trying to prove the new technique is an improvement over the old technique.

Part B: Identify the correct test and check the appropriate conditions.

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.)