1. Industrial lightbulbs should have a mean life length acceptable to potential users and a relatively small variation in life length. Large variations below the mean annoy customers; large variations above the mean reduce replacement sales. A random sample of 20 bulbs produced by a particular manufacturer produced the following lengths of life in hours: 2100, 2302, 1951, 2067, 2415, 1883, 2101, 2046, 2378, 2019, 1924, 2183, 1977, 2492, 2286, 2401, 2046, 2161, 2253, 1827. a) Calculate the mean, variance and standard deviation of the life length using the standard unbiased estimator. b) Calculate the 95% confidence interval for the mean and the variance estimates.