Golf balls must meet a set of five standards in order to be used in professional tournaments. One ofthese standards is distance traveled. When a ball is hit by a mechanical device, Iron Byron, with a 10-degree angle of launch, a backspin of 42 revolutions per second, and a ball velocity of 235 feet persecond, the distance the ball travels may not exceed 291.2 yards. Manufacturers want to develop balls thatwill travel as close to the 291.2 yards as possible without exceeding that distance. A particularmanufacturer has determined that the distances traveled for the balls it produces are normally distributedwith a standard deviation of 2.8 yards. This manufacturer has a new process that allows it to set the meandistance the ball will travel.

(a) If the manufacturer sets the mean distance traveled to be equal to 288 yards, what is theprobability that a ball that is randomly selected for testing will travel too far?

(b) Assume the mean distance traveled is 288 yards and that five balls are independently tested. What is the probability that at least one of the five balls will exceed the maximum distance of 291.2 yards?