a machine cuts plastic into sheets that are 50 feet 600 inch

a machine cuts plastic into sheets that are 50 feet (600 inches) long. inches) long. Assume that the population of lengths is normally distributed.

a. The company wants to estimate the mean length the machine is cutting the plastic within 0.125 inch. Determine the minimum sample size required to construct a 95% confidence interval for the population mean. Assume the poplulation standard deviation is 0.25 inch.

B. repeat part (a) using an error tolerance of 0.0625

Solution

a)

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 =    0.25  
E = margin of error =    0.125  
      
Thus,      
      
n =    15.36583528  
      
Rounding up,      
      
n =    16   [ANSWER]

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b)

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 =    0.25  
E = margin of error =    0.0625  
      
Thus,      
      
n =    61.46334113  
      
Rounding up,      
      
n =    62   [ANSWER]