A fair six-sided die will be rolled fifteen times, and the numbers that land face up will be recorded. Let x¯1x¯1 represent the average of the numbers that land face up for the first five rolls, and...

A fair six-sided die will be rolled fifteen times, and the numbers that land face up will be recorded. Let x¯1x¯1 represent the average of the numbers that land face up for the first five rolls, and let x¯2x¯2 represent the average of the numbers landing face up for the remaining ten rolls. The mean μμ and variance σ2σ2 of a single roll are 3.5 and 2.92, respectively. What is the standard deviation σ(x¯1−x¯2)σ(x¯1−x¯2) of the sampling distribution of the difference in sample means x¯1−x¯2x¯1−x¯2?

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  2.92+2.922.92+2.92

  
  

  
  
  
  
  A
  
  


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  2.92−2.922.92−2.92

  
  

  
  
  
  
  B
  
  


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  2.925+2.9210−−−−−−−−√2.925+2.9210

  
  

  
  
  
  
  C
  
  


• 
  
  
  

  
  

  2.9225+2.92210−−−−−−−−−−√2.9225+2.92210

  
  

  
  
  
  
  D
  
  


• 
  
  
  

  
  

  2.9225−2.92210−−−−−−−−−−√2.9225−2.92210

  
  

  
  
  
  
  E