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Problem 6. A random variable x has a Normal distribution with an unknown mean and a...

Problem 6. A random variable x has a Normal distribution with an unknown mean and a standard deviation of 12. Suppose that we take a random sample of size n = 36 and find a sample mean of "x-bar" = 98. What is a 95% confidence interval for the mean of x?

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Answer #1

We have given that,              
              
Sample mean =98      
Population standard deviation=12  
Sample size=36      
Level of significance =   0.05      
Z critical value (by using Z table)=1.96      
              
Confidence interval formula is              


=(94.08,101.92)  

       
Lower confidence limit =94.08  
Upper confidence limit =101.92  

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