A random sample of 36 locations in a western state yield an

A random sample of 36 locations in a western state yield an average annual precipitation of 17.6 inches for last year. Suppose the standard deviation is 2.4 inches If a meteorologist wants to estimate the rainfall m confidence, how large of a sample does she need to take? ean within .25 inch with 95% I, Font Sizes P

Solution

Note that      
      
n = z(alpha/2)^2 s^2 / E^2      
      
where      
      
alpha/2 = (1 - confidence level)/2 =    0.025  
      
Using a table/technology,      
      
z(alpha/2) =    1.959963985  
      
Also,      
      
s = sample standard deviation =    2.4  
E = margin of error =    0.25  
      
Thus,      
      
n =    354.0288449  
      
Rounding up,      
      
n =    355   [ANSWER]