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.

(co 3) the soup produced by a company has a salt level that is normally distributed with a mean of 5.4 grams and a standard deviation of 0.3 grams. the company takes readings of every 10th bar off the production line. the reading points are 5.8, 5.9, 4.9, 6.5, 5.0, 4.9, 6.2, 5.1, 5.7, 6.1. is the process in control or out of control and why? it is out of control as two of these data points are more than 2 standard deviations from the mean it is in control as the data points more than 2 standard deviations from the mean are far apart it is out of control as one of these data points is more than 3 standard deviations from the mean it is in control as the values jump above and below the mean