Consider the portfolio of legacy COBOL programs in the portfolio 
of some large financial institution. Assume that a "student t"
distribution with 9 degrees of freedom may be used to describe
the effort (man hours) spent maintaining each program in the 
portfolio over the past year. Assume also that the mean effort is 
280 with a std dev of 50.

a) Find the proportion of programs that required more than 360
   hours of maintenance.

   We need to use the transformation rule. Since t=(360-280)/50=1.6
   then we are interested in the proportion to the right of 1.6 for
   the standard student t with df=9. For the row indexed by 9, 1.6
   is between 1.383 and 1.833 and so the desired proportion is between 
   5% and 10%.

b) What if the degrees of freedom was 40 instead of 9. How would your 
   answer to part a) and part b) be different. Justify your answer.

   Since a "student t" with df>=30 is equivalent to the corresponding
   normal distribution, we may use the z table to determine the 
   desired proportion.

   The z value would also be 1.6 and so the desired proportion is 
   100%-94.52%=5.48%. This is as expected since for larger df the
   distribution has thinner tails and so we would expect a smaller
   proportion.