1. You are told that, for some population, the population parameters are mu=50 
   and sigma=5. Considering the sampling distribution of ybar, answer the 
   following:

   a) Assume samples of size n=26. What percentage of samples would you expect
      to have mean greater than 53 in this case. Make any necessary assumptions.

        Since n is small, assume y is normally distributed. Then ybar is 
        Student t with n-1=26-1=25df.
	s(ybar)=5/5=1 and so t=(53-50)/1=3. From the t table for 25 df
	the percentage is less than 0.5%.


2. You are told that, for some population, the population parameters are mu=80 
   and sigma=12. Considering the sampling distribution of ybar, answer the 
   following:
 
   a) Assume samples of size n=17. What percentage of samples would you expect
      to have mean less than 83 in this case. Make any necessary assumptions.

        Since n is small, assume y is normally distributed. Then ybar is 
        Student t with n-1=17-1=16df.
	s(ybar)=12/4=3 and so t=(83-80)/3=1. From the t table for 16 
	df this t value is bounded by 0.69 and 1.34 and so the desired 
        percentage is between 75% and 90%.