The average spending at Necos salad bar is 986 with a standa

The average spending at Neco\'s salad bar is $9.86 with a standard deviation of $3. The distribution follwos Normal distribution. The management is inersting in the middle 80% of the customers (spending wise) as it believes that they represent the customer base. What will be the difference between the upper and lower spending cut-offs which define the middle 80% of the customers?

Solution

Note that              
      
Lower Bound = X - z(alpha/2) * s / sqrt(n)              
Upper Bound = X + z(alpha/2) * s / sqrt(n)              
              
where              
alpha/2 = (1 - confidence level)/2 =    0.1          
X = sample mean =    9.86          
z(alpha/2) = critical z for the confidence interval =    1.281551566          
s = sample standard deviation =    3          
              
Thus,              

Lower bound =    6.015345303          

Upper bound =    13.7046547          
              
Thus, the difference between the upper and lower spending cut-offs which define the middle 80% of the customers is

13.7046547 - 6.015345303 = 7.689309397 [ANSWER]