Questions 26 and 27 refer to the following setup An electric

Questions 26 and 27 refer to the following setup: An electrical firm manufactures light bulbs that have length of life that is approximately normally distributed with a known standard deviation of 40 hours. A sample of 32 bulbs has an average life of 780 hours. 26. What is the upper limit of a 96% confidence interval for the population mean of all light bulbs produced by this firm?

Solution

26.

Note that              
                      
Upper Bound = X + z(alpha/2) * s / sqrt(n)              
              
where              
              
X = sample mean =    780          
z(alpha/2) = critical z for the confidence interval =    2.053748911          
s = sample standard deviation =    40          
n = sample size =    32          
              
Thus,              
              
Upper bound =    794.5221978 [ANSWER]

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27.

As the width upper - lower = 5 hrs, and as

margin of error (E) = (upper - lower)/2 = 2.5, then
      
Note that      
      
n = z(alpha/2)^2 s^2 / E^2      
      
where      
      
alpha/2 =    0.02  
      
Using a table/technology,      
      
z(alpha/2) =    2.053748911  
      
Also,      
      
s = sample standard deviation =    40  
E = margin of error =    2  
      
Thus,      
      
n =    1687.153835  
      
Rounding up,      
      
n =    1688   [ANSWER]