The operations manager of a large production plane would lik

The operations manager of a large production plane would like to the mean amount of time a worker takes to assemble a new electronic component. Assume that the standard deviation of this assembly time is 3.6 minutes and is normally distributed.

Solution

7.

a)

Note that              
Margin of Error E = z(alpha/2) * s / sqrt(n)              
Lower Bound = X - z(alpha/2) * s / sqrt(n)              
Upper Bound = X + z(alpha/2) * s / sqrt(n)              
              
where              
alpha/2 = (1 - confidence level)/2 =    0.04          
X = sample mean =    16.2          
z(alpha/2) = critical z for the confidence interval =    1.750686071          
s = sample standard deviation =    3.6          
n = sample size =    120          
              
Thus,              
Margin of Error E =    0.575334151          
Lower bound =    15.62466585          
Upper bound =    16.77533415          
              
Thus, the confidence interval is              
              
(   15.62466585   ,   16.77533415   ) [ANSWER]

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b)

Note that      
      
n = z(alpha/2)^2 s^2 / E^2      
      
where      
      
alpha/2 = (1 - confidence level)/2 =    0.04  
      
Using a table/technology,      
      
z(alpha/2) =    1.750686071  
      
Also,      
      
s = sample standard deviation =    3.6  
E = margin of error = 15/60 =    0.25  
      
Thus,      
      
n =    635.5380207  
      
Rounding up,      
      
n =    636   [ANSWER]

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c)

Note that              
Margin of Error E = t(alpha/2) * s / sqrt(n)              
Lower Bound = X - t(alpha/2) * s / sqrt(n)              
Upper Bound = X + t(alpha/2) * s / sqrt(n)              
              
where              
alpha/2 = (1 - confidence level)/2 =    0.04          
X = sample mean =    16.2          
t(alpha/2) = critical t for the confidence interval =    1.828051172          
s = sample standard deviation =    4          
n = sample size =    25          
df = n - 1 =    24          
Thus,              
Margin of Error E =    1.462440938          
Lower bound =    14.73755906          
Upper bound =    17.66244094          
              
Thus, the confidence interval is              
              
(   14.73755906   ,   17.66244094   ) [ANSWER]