XYZ Corp. hires a quality assurance consultant to assess the quality of a 
new software release. The release consists of several thousand modules. She 
selects a sample of these modules and determines the number of failures 
during beta testing. She finds the following:

       size (lines of code): mean = 1200; SD = 150
       # of failures: mean = 20; SD of 5
       correlation between size and # of failures = 0.6

The objective is to use regression methods to develop an equation to predict 
number of failures from program size. Assume normality where necessary.

1. About what proportion of programs had more than 28 failures.
 
2. Estimate the number of failures for a program of size 1100 lines of code.
 
3. Given the objective above, derive and state the regression equation.
 
4. Consider carefully the coefficients of the regression equation obtained 
for 3. Interpret these coefficients.
 
5. For programs of size 1100 lines, about what proportion had more than 28 
failures