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Suppose that X is normally distributed with known variance 95 and unknown mean. Five independent draws...

Suppose that X is normally distributed with known variance 95 and unknown mean. Five independent draws give X values of 46, 112, 85, 83 and 64. Find a 95% confidence interval for the mean.

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Answer #1

We have for given data,          
              
Sample mean =78      
Population standard deviation=9.75  
Sample size=5      
Level of significance =1-0.95=0.05      
Z critical value (by using Z table)=1.96      
              
Confidence interval formula is              


=(69.45,86.55)
          
Lower confidence limit =69.45  
Upper confidence limit =86.55

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