A database administrator (DBA) is interested in evaluating the performance 
of a new release of a database management system (DBMS). She runs a standard 
benchmark program several times and, for each run, measures the time to 
completion in seconds. She finds that the mean time required is 500 seconds 
with a standard deviation of 30 seconds. Assume that the distribution of 
times is normal.
 
1. What proportion of measured times would you expect to fall below 470 
seconds.
 
2. What proportion of measured times would you expect to fall between 520 
and 560 seconds.
 
3. For one of these measurements, the time is 450 seconds. Determine the 
percentile rank of this measurement.
 
4. Assume that adequate performance is achieved if 95%, or more, of these 
measurements are less than 554 seconds. Comment on the performance of the 
new release of the DBMS. Justify your answer.