A random sample of 101 light bulbs had a mean life of 481 ho

A random sample of 101 light bulbs had a mean life of 481 hours with a standard deviation of 30 hours. Construct a 90 percent confidence interval for the mean life, , of all light bulbs of this type. Interpret the interval!

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 =    0.05          
X = sample mean =    481          
z(alpha/2) = critical z for the confidence interval =    1.644853627          
s = sample standard deviation =    30          
n = sample size =    101          
              
Thus,              
              
Lower bound =    476.0899284          
Upper bound =    485.9100716          
              
Thus, the confidence interval is              
              
(   476.0899284   ,   485.9100716   ) [ANSWER]

Thus, we are 90% confident that the population mean life of the light bulbs is between 476.09 and 485.91 hours. [ANSWER]