Suppose that the standard deviation of the tube life for a particular brand of TV picture tube is known to be σ = 500, but the mean operating life is not known. Overall, the operating life of the tubes is assumed to be approximately normally distributed. For a sample of n = 15, the mean operating life is x = 8900 hours. Construct (a) the 95 percent and (b) the 90 percent confidence intervals for estimating the population mean.