The shape of the distribution of the time required to get an

The shape of the distribution of the time required to get an elephant ear at the state fair is unknown. However, records indicate that the standard deviation is 1.2 minutes. Suppose we wanted to estimate the mean time required to get an elephant ear within 1.5 minutes with 95% confidence. what size sample would be required? (show work please)

Solution

The central limit theorem can permit us to approximate the distirbution of the sample mean as a normal distirbution even if we do not know the shape of the original distribution.

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 =    1.2  
E = margin of error =    1.5  
      
Thus,      
      
n =    2.458533645  
      
Rounding up,      
      
n =    3   [ANSWER]

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This sample size is too low, so I am thinking that there is something wrong with the given. If there is some typo error here, please resubmit this question so we can continue helping you! Thanks!