Find the minimum sample size necessary to estimate the avera

Find the minimum sample size necessary to estimate the average time it takes a person to find a job with 95% confidence to be accurate to within E = 0.5 months of the actual time. Assume that the time to find a job is normally distributed with \\sigma= 1.8 months.

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 =    1.8  
E = margin of error =    0.5  
      
Thus,      
      
n =    49.78530632  
      
Rounding up,      
      
n =    50   [ANSWER]