A gigantic warehouse stores approximately 60 million empty aluminum beer and sod

Question

A gigantic warehouse stores approximately 60 million empty aluminum beer and soda cans. Recently, a fire occurred at the warehouse The smoke from the fire contaminated many of the cans with blackspot. rendering them unusable. A statistician was hired by the insurance company to estimate p. the true proportion of cans in the warehouse that were contaminated by the fire. How many aluminum cans should be randomly sampled to estimate p to within 0.07 with 90% confidence? The statistician should sample cans to estimate the proportion that were contaminated by the fire to within 0.07 with 90% confidence (Round up to the nearest can.)

Explanation / Answer

Note that      
      
n = z(alpha/2)^2 p (1 - p) / E^2      
      
where      
      
alpha/2 =    0.05  
As there is no previous estimate for p, we set p = 0.5.      
      
Using a table/technology,      
      
z(alpha/2) =    1.644853627  
      
Also,      
      
E =    0.07  
p =    0.5  
      
Thus,      
      
n =    138.0379313  
      
Rounding up,      
      
n =    139   [ANSWER]

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