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.

Answer 1

Here, n =10,000
Let p (the probability of getting a defective item) = 0.02
q =1-0.02 = 0.98

\[\text{Mean = Expected number of defective items } \]

\[ \Rightarrow np = 200\]

\[\text{ Variance}  (npq) = 200(0 . 98) \]

\[ = 196\]

\[\text{ Standard deviation } = \sqrt{\text{ Variance } } = 14\]

\[\text{ So, mean = 200 and standard deviation } = 14\]