Tianlang Guan was the youngest person ever to participate in the Masters Golf Tournament. The 14-year-old from China played the Augusta, Georgia, course with the confidence of a professional, but very slowly. He was warned about his slow play and was assessed a one-stroke penalty on the par-4 17th hole on the second day of the tournament.16 The PGA tour maintains a 40-second time limit to play a stroke, but also has several exceptions to this rule that allow for an additional 20 seconds. The mean time for all golf shots is 38 seconds.17 Assume the time for all golf shots is normally distributed with standard deviation 9 seconds, and suppose a golf shot is selected at random.
a. What is the probability that a randomly selected shot takes between 25 and 35 seconds?
b. If the shot takes more than 60 seconds, the golfer is assessed a penalty stroke. What is the probability that the golfer will be assessed a penalty stroke?
c. Suppose a golfer takes 72 strokes to complete the round. What is the probability that at least 60 of these shots take less than 45 seconds?
The International Tennis Federation (ITF) establishes the specifications for tennis balls. The diameter of a tennis ball used in any tournament must be between 2.5 and 2.625 inches. Suppose the diameter of a tennis ball is approximately normal with mean 2.5625 inches and standard deviation 0.04 inch.
a. What is the probability that a randomly selected tennis ball will meet ITF diameter specifications?
b. Suppose six tennis balls will be used in a tournament game. What is the probability that exactly one will not meet ITF diameter specifications? Assume independence.