Diastolic blood pressure levels in an adult population have

Diastolic blood pressure levels in an adult population have mean Mu = 90 and variance sigma^2 = 144 (so sigma = 12). Using the CLT, how large a sample size, n, should I take so that, with probability 0.99, my sample Mean,X, is between 87.43 and 92.57?

Solution

Here, the margin of error is

upper bound - mean = E = 2.57

Note that      
      
n = z(alpha/2)^2 s^2 / E^2      
      
where      
      
alpha/2 =    0.005  
      
Using a table/technology,      
      
z(alpha/2) =    2.575829304  
      
Also,      
      
s = sample standard deviation =    12  
E = margin of error =    2  
      
Thus,      
      
n =    238.8562776  
      
Rounding up,      
      
n =    239   [ANSWER]