Four hundred randomly selected working adults in a certain s

Four hundred randomly selected working adults in a certain state, including those who worked at home, were asked the distance from their home to their workplace. The average distance was 8.84 miles with standard deviation 2.70 miles. Construct a 99% confidence interval for the mean distance from home to work for all residents of this state.

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 =    8.84          
z(alpha/2) = critical z for the confidence interval =    2.575829304          
s = sample standard deviation =    2.7          
n = sample size =    400          
              
Thus,              
Margin of Error E =    0.347736956          
Lower bound =    8.492263044          
Upper bound =    9.187736956          
              
Thus, the confidence interval is              
              
(   8.492263044   ,   9.187736956   ) [ANSWER]