A quality control manager at factory manufacturing high intensity light bulbs which have relatively short lifetime but maintain their intensity during their lifetime needs to estimate the average life of a light bulb. It is known that the process lifetime is normally distributed and has a standard deviation of 180 hours. A sample of 20 light bulbs gives a mean life of 236 hours.
a. Find a 95% confidence interval for the process mean lifetime and give an interpretation of this interval.
b. What sample size needs to be used if the mean lifetime is to be estimated within an error of plus or minus 24 hours with probability 0.9?