Normal Distribution Problems:

1. For some population the measurement of interest has mean mu=0 and 
   standard deviation sigma=1. Assume that these measurements are 
   normally distributed. Complete the following:
   a) Determine the proportion of measurements greater than 3.00. 
   b) Determine the proportion of measurements less than -2.53. 
   c) Determine the proportion of measurements greater than -0.76.

2. Assume that the wait time (ms) of database transactions for some DBMS
   is normally distributed with mean mu=60.0ms and standard deviation 
   sigma=10.0ms.
   a) Find the proportion of transactions that waited for between 36.0ms
      and 48.0ms. 
   b) Find the proportion of transactions that waited for less than
      15.2ms. 
   c) Consider the wait time 41.5ms. Determine the percentile rank for
      this wait time.
   d) Determine the wait time that defines the 25th percentile. 

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=2. 
   b) Determine the proportion of measurements less than -2.53, if df=12. 
   c) Determine the proportion of measurements greater than -0.76, if df=25.

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.