A certain company makes light fixtures on an assembly line A

A certain company makes light fixtures on an assembly line. An efficiency expert wants to determine the mean time it takes an employee to assemble the switch on one of these fixtures. A preliminary study used a random sample of 45 observations and found that the sample standard deviation was s=78 seconds. How many more observations are necessary for the efficiency expert to be 97% sure that the point estimate of the true mean will be off by at most 15 seconds.

Solution

Note that      
      
n = z(alpha/2)^2 s^2 / E^2      
      
where      
      
alpha/2 = (1 - confidence level)/2 =    0.015  
      
Using a table/technology,      
      
z(alpha/2) =    2.170090378  
      
Also,      
      
s = sample standard deviation =    78  
E = margin of error =    15  
      
Thus,      
      
n =    127.3392624  
      
Rounding up,      
      
n =    128  

Thus, we need 128 - 45 = 83 more. [ANSWER, 83]