Industrial light bulbs should have a mean life length acceptable to potential users and a relatively  small variation in life length. If some bulbs fail too early in their life, users become annoyed and are  likely to switch to bulbs produced by a different manufacturer. Large variations above the mean  reduce replacement sales; in general, variation in life lengths disrupts the user’s replacement  schedules. 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, 2146, 2278, 2019,  1924, 2183, 2077, 2392, 2286, 2501, 1946, 2161, 2253, 1827. (a) Find a 99% confidence interval for the standard deviation of the lengths of life for the bulbs  produced by this manufacturer.  (b) Is the true population standard deviation possibly less than 150 hours? Why or why not?

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