A design engineer wants to construct a sample mean chart for controlling the service life of a halogen headlamp his company produces. He knows from numerous previous samples that when this service life is in control it is normally distributed with a mean of 500 hours and a standard deviation of 20 hours. On three recent production batches, he tested service life on random samples of four headlamps, with these results: Compute the Upper Control Limit for the Mean chart

Sample 1 490 Service Life (hours) 500 500 515 530 480 490 2 520 500 515 470 3 475