Assume that the helium porosity in percentage of coal sample

Assume that the helium porosity (in percentage) of coal samples taken from any particular seam is normally distributed with true population standard deviation 0.75. Compute a 95% CI for the true average porosity of a certain seam if the average porosity for 20 specimens from the seam was 4.85.

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 =    0.025          
X = sample mean =    4.85          
z(alpha/2) = critical z for the confidence interval =    1.959963985          
s = sample standard deviation =    0.75          
n = sample size =    20          
              
Thus,              
Margin of Error E =    0.328695953          
Lower bound =    4.521304047          
Upper bound =    5.178695953          
              
Thus, the confidence interval is              
              
(   4.52   ,   5.18   ) [ANSWER, A]