The quantity of gasoline purchased in a single sale at a cha

The quantity of gasoline purchased in a single sale at a chain of filling stations in a certain region is normally distributed with mean 11.6 gallons and standard deviation 2.78 gallons. Find the three quartiles for the quantity of gasoline purchased in a single sale

Solution

The quartiles correspond to the 25th, 50th, and 75th percentiles.

Thus, for the 1st quartile:

First, we get the z score from the given left tailed area. As          
          
Left tailed area =    0.25      
          
Then, using table or technology,          
          
z =    -0.67448975      
          
As x = u + z * s,          
          
where          
          
u = mean =    11.6      
z = the critical z score =    -0.67448975      
s = standard deviation =    2.78      
          
Then          
          
x = critical value =    9.724918494   [ANSWER, FIRST QUARTILE]

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For the second quartile (median):

First, we get the z score from the given left tailed area. As          
          
Left tailed area =    0.5      
          
Then, using table or technology,          
          
z =    0      
          
As x = u + z * s,          
          
where          
          
u = mean =    11.6      
z = the critical z score =    0      
s = standard deviation =    2.78      
          
Then          
          
x = critical value =    11.6   [ANSWER, SECOND QUARTILE OR MEDIAN]

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For the third quartile:

First, we get the z score from the given left tailed area. As          
          
Left tailed area =    0.75      
          
Then, using table or technology,          
          
z =    0.67448975      
          
As x = u + z * s,          
          
where          
          
u = mean =    11.6      
z = the critical z score =    0.67448975      
s = standard deviation =    2.78      
          
Then          
          
x = critical value =    13.47508151   [ANSWER, THIRD QUARTILE]