The life in hours of a 100watt light bulb is known to be app

The life in hours of a 100-watt light bulb is known to be approximately normally distributed with standard deviation s = 25 hours. A random sample of 20 bulbs has a mean life of 1014 hours.

A. Construct a 95% two-sided confidence interval on the mean life

B. Construct a 95% lower confidence interval on the mean life

C. Suppose we wanted the total width of the two-sided confidence interval on the mean life of the bulbs to be 6 hours at 95% confidence, what sample size should be used?

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 =    1014          
z(alpha/2) = critical z for the confidence interval =    1.959963985          
s = sample standard deviation =    25          
n = sample size =    20          
              
Thus,              
              
Lower bound =    1003.043468          
Upper bound =    1024.956532          
              
Thus, the confidence interval is              
              
(   1003.043468   ,   1024.956532   )

**************************************

Hi! Please submit the next part as a separate question. That way we can continue helping you! Thanks!