The operation manager at a tire manufacturing company believes that the mean mileage of a tire is 49,360 miles, with a variance of 6,568,969. What is the probability that the sample mean would differ from the population mean by less than 231 miles in a sample of 247 t ires if the manager is correct? Round your answer to four decimal places.

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.)