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Question
The probability that an item produced by a factory is defective is 0.02. A shipment of 10,000 items is sent to its warehouse. Find the expected number of defective items and the standard deviation.
Solution
Here, n =10,000
Let p (the probability of getting a defective item) = 0.02
q =1-0.02 = 0.98
\[\text{Mean = Expected number of defective items } \]
\[ \Rightarrow np = 200\]
\[\text{ Variance} (npq) = 200(0 . 98) \]
\[ = 196\]
\[\text{ Standard deviation } = \sqrt{\text{ Variance } } = 14\]
\[\text{ So, mean = 200 and standard deviation } = 14\]
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