A normallydistributed population has a mean 149 and a stand

A normally-distributed population has a mean = 149 and a standard deviation = 16. For a set of samples of size 14 taken from this population, about 95.5% of the means will be in what interval?

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 =    0.0225          
X = sample mean =    149          
z(alpha/2) = critical z for the confidence interval =    2.004654462          
s = sample standard deviation =    16          
n = sample size =    14          
              
Thus,              
Margin of Error E =    8.572263057          
Lower bound =    140.4277369          
Upper bound =    157.5722631          
              
Thus, the confidence interval is              
              
(   140.4277369   ,   157.5722631   ) [ANSWER]