Answer:
x=4
Step-by-step explanation:
checked my answer its right
 
        
             
        
        
        
327421537466 and yes i did all of this that fast 
        
                    
             
        
        
        
Answer:
Let X the random variable that represent the variable of interest of a population, and for this case we know the distribution for X is given by:
 
  
Where  and
 and  
And for this case we select a sample size of n= 81. Since the distribution for X is normal then we know that the distribution for the sample mean  is given by:
 is given by:
 
And the standard error of the mean would be:

4.1.5
Step-by-step explanation:
Previous concepts
Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".
The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".  
Solution to the problem
Let X the random variable that represent the variable of interest of a population, and for this case we know the distribution for X is given by:
 
  
Where  and
 and  
And for this case we select a sample size of n= 81. Since the distribution for X is normal then we know that the distribution for the sample mean  is given by:
 is given by:
 
And the standard error of the mean would be:

4.1.5
 
        
             
        
        
        
Let x be the distance from Syracuse where they pass. The first car travels a distance of x in time x/65 while the second car travels a distance 240-x in time (240-x)/55. They pass at the same time after leaving their starting points so x/65=(240-x)/55.
Cross-multiplying we get: 55x=65(240-x)=15600-65x, 120x=15600, x=15600/120=130 miles.
They pass 130 miles from Syracuse.
        
             
        
        
        
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