One hundred tractor trailer trucks are weighed at a highway

One hundred tractor

-

trailer trucks are weighed at a highway weigh station from a normal

population. The average weight is 50,000 pounds with a standard deviation of 3600

pounds. Construct a 99% confidence interval for the ave

rage weight of the trucks in the

population.

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 =    0.005          
X = sample mean =    50000          
z(alpha/2) = critical z for the confidence interval =    2.575829304          
s = sample standard deviation =    3600          
n = sample size =    100          
              
Thus,              
Margin of Error E =    927.2985493          
Lower bound =    49072.70145          
Upper bound =    50927.29855          
              
Thus, the confidence interval is              
              
(   49072.70145   ,   50927.29855   ) [ANSWER]