If the population standard deviation of the lifetime of a va

If the population standard deviation of the lifetime of a vacuum cleaner is 300 hours, how large of a sample must be taken in order to be 99% confident that the margin of error will not exceed 50 hours?

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 =    300  
E = margin of error =    50  
      
Thus,      
      
n =    238.8562776  
      
Rounding up,      
      
n =    239   [ANSWER]