Student t Distribution Problems:

1. For some population the measurement of interest has mean mu=0 and 
   standard deviation sigma=1. Assume that these measurements are 
   "student t" distributed. Complete the following:
   a) Determine the proportion of measurements greater than 3.00, if df=1. 
   b) Determine the proportion of measurements greater than 3.55, if df=12. 
   c) Determine the proportion of measurements less than 1.75, if df=24.

2. Workstations based on the latest Motorola PowerPC G4 CPU achieve a mean 
   "MIPS rating" of mu=1500 with standard deviation sigma=20. Assume that 
   "MIPS rating" is "student t" distributed with 4 degrees of freedom (df).
   a) Find the proportion of workstations that achieved a "MIPS rating" more 
      than 1540. 
   b) Find the proportion of workstations that achieved a "MIPS rating" less 
      than 1560. 
   c) You are told that "MIPS rating" is "student t" distributed with 34 df 
      instead of 4 df. Would this change in df affect your answer to part b) 
      above? Justify your answer.



Sampling Distribution (ybar) Problems:

A colleague at a local company is interested in evaluating the performance 
of the database management system and decides to examine transaction service 
time (y) for transactions processed over a certain period. Transaction 
service time is the time in milliseconds that transactions wait in the 
transaction queue for service. Given this population, assume the following 
parameters:

       Mean: mu(y)=120 milliseconds
       Standard deviation: sigma(y)=20 milliseconds

Considering the sampling distribution of ybar, complete the following. Make 
and state any necessary assumptions. 

1. Consider samples of size n=17.
   a) What proportion of samples would you expect to result in sample means 
      greater than 128 milliseconds. 
   b) What proportion of samples would you expect to result in sample means 
      less than 122 milliseconds. 

2. Consider samples of size n=100. 
   a) What proportion of samples would you expect to result in sample means 
      greater than 128 milliseconds. 
   b) What proportion of samples would you expect to result in sample means 
      between 115 milliseconds and 118 milliseconds.