The coffee company American Expresso has a promotion where i

The coffee company American Expresso has a promotion where \"if you don\'t get your take away coffee within 180 seconds, it,s free!\". American Expresso has commissioned an independent study which found that the time to prepare a take away coffee at one of their stores is approximately normally distributed with a mean time of 156 seconds and a standard deviation of 21 seconds. You may find this standard normal table useful throughout the following questions.

Solution

A)

We first get the z score for the critical value. As z = (x - u) sqrt(n) / s, then as          
          
x = critical value =    180      
u = mean =    156      
          
s = standard deviation =    21      
          
Thus,          
          
z = (x - u) / s =    1.142857143      
          
Thus, using a table/technology, the right tailed area of this is          
          
P(z >   1.142857143   ) =    0.126548954 or 12.7% [ANSWER]

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B)

First, we get the z score from the given left tailed area. As          
          
Left tailed area =    0.975      
          
Then, using table or technology,          
          
z =    1.959963985      
          
As x = u + z * s / sqrt(n)          
          
where          
          
u = mean =    156      
z = the critical z score =    1.959963985      
s = standard deviation =    21      
          
Then          
          
x = critical value =    197.1592437 = 197 s [ANSWER]