Monday: Back to the Grind!

Back to work!

Tonight, please complete the AP problem provided in class (or in blue below)! The homework answers are next to each question in pink.

Also, don't forget--if you any anything to make up (homework and/or quizzes--ALL MAKEUP HW/QUIZZES MUST BE DONE BY WEDNESDAY (or after school Weds.)!

AP Problem: Using Probability

Some golf balls are required to meet a set of five standards to be used in professional tournaments. One of these is the distance traveled. A ball 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 ft/sec, should not exceed a distance of 291.2 yards. Companies hope to develop balls that will travel as close to this 291.2 distance as possible, without exceeding it. One manufacturer has determined the distances are normally distributed with a standard deviation of 2.8 yards. This manufacturer has a new process that allows it to set the mean distance the ball will travel.

1. Suppose the manufacturer sets the mean distance to 288 yards; calculate the probability that a randomly selected ball travels too far. (0.1265)
2. Suppose the mean distance is 288 yards and that five balls are independently tested. Calculate the probability that at least one of the five balls will exceed the max distance of 291.2 yards. (0.4915)
3. The manufacturer wants to be 99% sure a randomly selected ball will not exceed the maximum distance of 291.2 yards; what is the largest mean that can be used in the manufacturing process? (284.69 ft; first, you have to use invnorm( to find what z-score has 99% of the data below it. Remember, to do this, we go to invnorm( on our calculator; the "area" is the % to the left, or .99. For mu and sigma we want to enter 0 and 1 because we want a z score. Now, we know the z-score of 2.326 has 99% of the data below it. We can sub the z-score, x, and Sx into the z-score formula and solve for the mean to find this answer).