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. 1. 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. 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.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