Question

Use the central limit theorem to find the mean and standard error of the mean of the indicated sampling distribution: The amounts body temperatures of patients with influenza (in degrees Fahrenheit) are normally distributed with a mean of 101 degrees and a standard deviation of 0.5 degrees. Random samples of size 9 are drawn from the population and the mean of each sample is determined.

		101 degrees; 0.1667 degrees
		101 degrees; 0.5000 degrees
		11.22 degrees; 0.1667 degrees
		11.22 degrees; 0.5000 degrees

Answer 1

As per Central Limit Theorem, for any distribution with mean µ and standard deviation σ,                    
as the sample size increases, the sampling distribution of the mean, X-bar,                   
can be approximated by a normal distribution with mean µ and standard error of the mean σ/√n where                  
n is the sample size                  
Let X be the body temperatures of patients with influenza                  
Given                  
Mean of X , µ = 101 degrees                  
Standard Deviation , σ = 0.5 degrees                  
n = 9                  
Thus the sample mean X̅ follows Normal Distribution with                   
mean    μ = 101 degrees   and standard error of the mean            σ = 0.5/√9 = 0.1667
                  
Answer : (Option 1)                  
              

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