please help with the following stats question A quality control engineer Is conc

Question

please help with the following stats question

A quality control engineer Is concerned about the breaking strength of surgical metal wire manufactured to stringent specifications. A sample of 25 Is randomly selected and the breaking strengths are recorded. The breaking strengths are considered to be normally distributed with a standard deviation of 3. Find a 95% confidence Interval for the mean breaking strength of the wire. The following represents the recorded breaking strengths of the sample: 26 27 18 23 24 20 21 24 19 27 25 20 24 21 26 19 21 20 25 20 23 25 21 20 21

Explanation / Answer

Note that              
              
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 =    0.025          
X = sample mean =    22.4          
z(alpha/2) = critical z for the confidence interval =    1.959963985          
s = sample standard deviation =    3          
n = sample size =    25          
              
Thus,              
              
Lower bound =    21.22402161          
Upper bound =    23.57597839          
              
Thus, the confidence interval is              
              
(   21.22402161   ,   23.57597839   ) [ANSWER]

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