total population=5000
n=100 

1. Average defect density for the sample is 0.4; standard deviation of 0.1. 

a) Estimate the defect density for the software product.
 
 	0.4
 
b) Compute the error in your estimate.
 
 	0.1/sqrt(100)=0.01
 
c) Derive a 90% confidence interval for defect density of the software product.
 
 	0.4 plus/minus 1.65(0.01)
 	[0.3835, 0.4165]
 
d) Interpret the confidence interval computed above.
 
 	The analysts should be 90% confident that the true
 	defect density is between 0.3835 and 0.4165
 
e) What if the analyst had selected a sample of 26 modules. Derive the 90% 
   confidence interval in this case. 
 
        0.1  plus/minus 1.71(0.02)
 	[0.3658, 0.4342]
 
 
2. 20 in sample have chronic performance problems and have to be rewritten. 

a) Estimate the proportion of modules with chronic performance problems in 
   the software product. 
 
 	0.2
 
b) Compute the error in your estimate.
 
 	sqrt(0.2(0.8)/100)=0.04
 
c) The development manager claims that it costs $1500 on average to code 
   and test each module. Estimate the rewrite cost due to performance problems. 
 
 	1500*0.2*5000=$1500000
 
d) Derive a 95% confidence interval for the proportion of modules with 
   chronic performance problems.
 
 	0.2 plus/minus 1.95(0.04)
 	[0.122, 0.278]
 
e) The development manager claims that only 10% of modules needed to be 
   rewritten because of performance problems. Given the confidence interval 
   computed above what can you say about this claim.
 
       Since the 95% confidence interval has a lower bound
       of 12.2% the analyst has strong evidence to say that 
       10% is too low and the development manager is 
       probably incorrect.