Using Binomial Probabilities in Baseball 95 Using Binomial Probabilities in Baseball This activity involves finding the probability of breaking a homerun record using simulations and the binomial probability formula. Just how unusual was it when Mark McGuire broke the homerun record in 19987 In 1998 the baseball world was enthralled by the epic chase of Mark McGuire and Sammy Sosa to surpass the single-season homerun record of 61 set by Roger Maris in 1961. L, a. Prior to his prolific 1998 season in which he shattered Roger Maris' single season homerun record of 61 by hitting 70 \"round-trippers,\" Mark McGuire averaged 1 homerun every 11.9 at-bats. Assuming this rate of homerun hitting applied to the 1998 season, determine the probability McGuire hits a homerun during a randomly selected at-bat in 1998. b. Open the Baseball Applet at www pearsonhighered.com/sullivanstats or from StatCrunch, open the Coin Flipping Applet. Enter the probability determined in part (a) in the \"Probability of heads\" cell. Under the number of coins, enter 600 to represent the typical number of at-bats during the season for a starting player. Run a total of 20 repetitions by clicking *\"5 runs\" four times. What does each of these 20 repetitions represent? Based on the graph, how many of the repetitions result in 62 or more homeruns (indicating Maris' record is broken)? c. There are a number of players who have averaged 1 homerun every 11.9 at-bats since Maris set his record. Increase the number of repetitions to 1,000 with the number of tosses at 600. What does each of these 1,000 repetitions represent? d. In the cell \"As extreme as,\" enter = 62 and select \"Count.\" This will allow us to determine the likelihood of a player hitting 62 or more homeruns in a season to break Maris' record. 96 Using Binomial Probabilities in Baseball 2. a. Use the binomial probability formula to compute the exact probability of Mark McGuire breaking Maris' record over the course of a 20-season career assuming he averages 1 homerun every 11.9 at-bats. b. What does this probability change to if McGuire is able to increase his homerun rate to 1 homerun every 10.8 at-bats? This was McGuire's homerun rate in 1998. C. Use the binomial probability formula to compute the exact probability of any particular player (who averages 1 homerun every 11.9 at-bats) with 600 at-bats breaking Maris' record. 3. a. Over the past few years, the prolific homerun hitters have been averaging 1 homerun every 13 at-bats. Assuming the league has 10 prolific homerun hitters in any given season, what is the likelihood of McGuire's record being broken in the next 20 years? Assume 600 at-bats per year. Answer using a simulation: Answer using the binomial probability formula: b. What homerun rate would be required among the top 10 homerun hitters in order for there to be at least a 5% chance of breaking McGuire's record within the next 20 years? Assume 600 at-bats per year