During an 8-hour shift of golf-ball production, one golf ball is randomly selected from each 2 minutes’ worth of output. The ball is then tested for “liveliness” by rolling it down a grooved, stainless- steel surface. At the bottom, it strikes a smooth iron block and bounces backward, up a gradually sloped, grooved surface inscribed with distance markings. The higher the ball gets on the rebound surface, the more lively it is.
1. A driving range has just purchased 100 golf balls. Use the computer and the binomial distribution in determining the individual and cumulative probabilities for x = the number of balls that scored at least 31.00 inches on the “bounce” test.
2. Repeat part (1), but use the normal approximation to the binomial distribution. Do the respective probabilities appear to be very similar?
3. Given the distribution of bounce test scores described above, what score value should be exceeded only 5% of the time? For what score value should only 5% of the balls do more poorly?
4. What is the probability that, for three consecutive balls, all three will happen to score below the lower of the two values determined in part (3)? Two hundred forty golf balls have been subjected to the bounce test during the most recent 8-hour shift. From the 1st through the 240th, their scores are provided in computer data file CDB07 as representing the con tinuous random variable, BOUNCE. The variable BALL is a sequence from 1 to 240.
5. Using the computer, generate a line graph in which BOUNCE is on the vertical axis and BALL is on the horizontal axis.
6. On the graph obtained in part (5), draw two horizontal lines—one at each of the BOUNCE scores determined in part (3).
7. Examining the graph and the horizontal lines drawn in part (6), does it appear that about 90% of the balls have BOUNCE scores between the two horizontal lines you’ve drawn, as the normal distribution would suggest when μ = 30.00 and σ = 2.00?
8. Comparing the BOUNCE scores when BALL = 1 through 200 to those when BALL = 201 through 240, does it appear that the process may have changed in some way toward the end of the work shift? In what way? Does it appear that the machine might be in need of repair or adjustment? If so, in what way should the adjustment alter the process as it appeared to exist at the end of the work shift?