Suppose you want to determine the average home run percentag

Suppose you want to determine the average home run percentage for the Royals baseball team. You randomly select 48 players from Royals history and determine that the mean number of home runs per 100 times at bat is 7.64

Solution

Note that      
      
n = z(alpha/2)^2 s^2 / E^2      
      
where      
      
alpha/2 = (1 - confidence level)/2 =    0.005  
      
Using a table/technology,      
      
z(alpha/2) =    2.575829304  
      
Also,      
      
s = sample standard deviation =    5.55  
E = margin of error =    1  
      
Thus,      
      
n =    204.3714026  
      
Rounding up,      
      
n =    205   [ANSWER, C]