Baseball America has noticed the number of homeruns has been increasing in recent years in the MLB. They want to develop a 95% confidence interval that captures the true home run percentage. Home run percentage is defined as the number of home runs per 100 at bats. To do so, they randomly selected 64 current MLB players and calculated their homeruns per at bat for the previous year, and obtained a sample mean and sample standard deviation of 2.2 and 1.7, respectively. a. Compute a 95% confidence interval for the population mean of the home run rate for all MLB players. Interpret with context to the problem. b. The home run percentages for three MLB players are:Player 1: Primetime Peanuts: 2.1Player 2: Spleens "No Pop" McGillicuddy: 4Player 3: Big Dog Lebowski: 1.5Assess the confidence interval you calculated and describe how the home run rate for these three players compare to the interval calculated for the population mean. c. If the confidence level was increased to 99%, would the interval be wider or narrower? Why?d. Before collecting any data, Baseball America wants to achieve a maximum bound on error of 0.3. They suspect the range of home run rates to be 1.5 to 8. How large a sample should be used to be 95% confident of achieving this level of accuracy?