A quality control engineer believes that the life of light bulbs for his company is normally distributed with a standard deviation of 100 h. A random sample of 10 light bulbs gives the following information on the life of the light bulbs: 1.000 h; 1,200 h; 600 h; 400 h; 900 h; 500 h; 1,520 h; 1,800 h; 300 h; 525 h

(a) Find a 90 % confidence interval for the mean life of the light bulbs.

(b) Suppose the standard deviation is not known. Construct a 90 % confidence interval for the mean life of the light bulbs.