it is known from past experience that the life of traffic li

it is known from past experience that the life of traffic lights bulbs is normally distrbuted with a standard deviation of 270 hours . in a study, if it is required to be 90% certain that the mean estimate is within 115 hours of the population mean. how many lights bulbs should be selected for the study?

Solution

Note that      
      
n = z(alpha/2)^2 s^2 / E^2      
      
where      
      
alpha/2 = (1 - confidence level)/2 =    0.05  
      
Using a table/technology,      
      
z(alpha/2) =    1.644853627  
      
Also,      
      
s = sample standard deviation =    270  
E = margin of error =    115  
      
Thus,      
      
n =    14.91373292  
      
Rounding up,      
      
n =    15   [ANSWER]