A random sample of 56 fluorescent light bulbs has a mean lif

A random sample of 56 fluorescent light bulbs has a mean life of 645 hours. Assume the population standard deviation is 31 hours. Construct a 95% confidence interval for the population mean.

A. (539.6, 551.2)

B. (636.9, 653.1)

C. (712.0, 768.0)

D. (112.0, 118.9)

Solution

Note that              
              
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 =    645          
z(alpha/2) = critical z for the confidence interval =    1.959963985          
s = sample standard deviation =    31          
n = sample size =    56          
              
Thus,              
              
Lower bound =    636.8807527          
Upper bound =    653.1192473          
              
Thus, the confidence interval is              
              
(   636.8807527   ,   653.1192473   ) [ANSWER, OPTION B]