The designer of a garbage truck that lifts rollout container

The designer of a garbage truck that lifts roll-out containers must estimate the mean weight the truck will lift at each collection point. A random sample of 325 containers of garbage on current collection routes yielded x=75.3 lb, s = 12.8 lb. Construct a 99.8% confidence interval for the mean weight the trucks must lift each time.

Solution

Note that              
Margin of Error E = z(alpha/2) * s / sqrt(n)              
Lower Bound = X - z(alpha/2) * s / sqrt(n)              
Upper Bound = X + z(alpha/2) * s / sqrt(n)              
              
where              
alpha/2 = (1 - confidence level)/2 =    0.001          
X = sample mean =    75.3          
z(alpha/2) = critical z for the confidence interval =    3.090232306          
s = sample standard deviation =    12.8          
n = sample size =    325          
              
Thus,              
Margin of Error E =    2.194115157          
Lower bound =    73.10588484          
Upper bound =    77.49411516          
              
Thus, the confidence interval is              
              
(   73.10588484   ,   77.49411516   ) [ANSWER]