The pulmonary blood that flows through this patient's right lung is
well oxygenated.  The pulmonary blood flowing through the left lung is
not oxygentated at all; that is, a right-to-left shunt exists due to a
mis-intubation where the endotracheal tube was accidentally inserted
into the right mainstem bronchus causing the right lung to be
over-ventilated and the left lung not ventilated at all.

Complete the table to show the conditions in the blood leaving the
left and right lungs and the conditions in the patient's mixed
arterial blood.  In completing this table, assume that 3/4 of the
pulmonary blood is to the right lung, and 1/4 of the flow is to the
left lung.  FIO2 .21.
            
             patient's venous    blood leaving  blood leaving     mixed  
              blood              Left lung      right lung       artieral blood
pO2 (mm Hg)   36
O2 at (%)     67

NOTE that the presence of the shunt had a big effect on the arterial
pO2.  Would you expect a similarly large effect on the arterial pCO2? 
Why or why not?

Here's a stab:

pO2 (mm Hg):
Patient's Venous Blood:  36 (Given)
Blood Leaving the left lung:  36 (Since there is no gas exchange)
Blood leaving the right lung:  100 (the normal alveolar pO2 in a well
oxygenated lung)
Mixed arterial blood:  = [36(.25) + 100(.75)] = 84 mm HG

To calculate the oxygen saturation in percentage, you need to know the
oxygen dissociation curve for this patient - which is dependant upon
the pH and temp.  I used the following website to make the conversion:
http://www.health.adelaide.edu.au/paed-anaes/javaman/Respiratory/oxygen/O2Values.html
or you may try this website as well:
http://www-users.med.cornell.edu/~spon/picu/calc/o2satcal.htm

In any case, here are the O2 % saturation values:
Patient's Venous Blood:  67 % (Given)
Blood Leaving the left lung:  67%
Blood leaving the right lung:  98% 
Mixed arterial blood:  96%

I hope that's correct.  Hopefully someone can check my math and claim the prize.