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Suppose that a widget manufacturing plant has two production systems working in parallel to produce widgets. The rst widget system is older, and produces 10000 widgets a day, with each widget being defective with probability 0.005, independently. The second widget system is brand new, and produces 25000 widgets a day, with each widget being defective with probability 0.002, independently. Moreover, the systems operate independently. At the end of each day, all of the day's widgets are collected together in a box.
Let X and Y be the number of widgets the rst and second system produce per day, respectively.
(a) What are the expectations and variances of X and Y?
(b) Using the central limit theorem and the table of the standard normal cdf, approximate the probability that more than 110 defective widgets are made in a day.
Attachment:- stat.pdf
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