Question

A random sample is selected from a population with mean μ = 102 and standard deviation...

A random sample is selected from a population with mean μ = 102 and standard deviation σ = 10. Determine the mean and standard deviation of the x sampling distribution for each of the following sample sizes. (Round the answers to three decimal places.)

(a) n = 12
μ =  
σ =  

(b) n = 13
μ =  
σ =  

(c) n = 37
μ =  
σ =  

(d) n = 70
μ =  
σ =  

(f) n = 140
μ =  
σ =  

(e) n = 560
μ =  
σ =

Homework Answers

Answer #1

Solution :

Given that mean μ = 102 and standard deviation σ = 10

(a) n = 12

The sampling distribution of x is

=> Mean μx = 102

=> standard deviation σx = σ/sqrt(n) = 10/sqrt(12) = 2.887

(b) n = 13

The sampling distribution of x is

=> Mean μx = 102

=> standard deviation σx = σ/sqrt(n) = 10/sqrt(13) = 2.774

(c) n = 37

The sampling distribution of x is

=> Mean μx = 102

=> standard deviation σx = σ/sqrt(n) = 10/sqrt(13) = 1.644

(d) n = 70

The sampling distribution of x is

=> Mean μx = 102

=> standard deviation σx = σ/sqrt(n) = 10/sqrt(70) = 1.195

(f) n = 140

The sampling distribution of x is

=> Mean μx = 102

=> standard deviation σx = σ/sqrt(n) = 10/sqrt(140) = 0.845

(e) n = 560

The sampling distribution of x is

=> Mean μx = 102

=> standard deviation σx = σ/sqrt(n) = 10/sqrt(560) = 0.423


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