If X 75 S 24 and n 36 and assuming that the population is

If X = 75, S = 24, and n = 36, and assuming that the population is normally distributed, construct a 95% confindence interval estimate for the population mean, µ.

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 =    75          
z(alpha/2) = critical z for the confidence interval =    1.959963985          
s = sample standard deviation =    24          
n = sample size =    36          
              
Thus,              
Margin of Error E =    7.839855938          
Lower bound =    67.16014406          
Upper bound =    82.83985594          
              
Thus, the confidence interval is              
              
(   67.16014406   ,   82.83985594   ) [ANSWER]