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Question
If on an average 9 ships out of 10 arrive safely at ports, find the mean and S.D. of the ships returning safely out of a total of 500 ships.
Solution
Total number of ships (n) = 500
Let X denote the number of ships returning safely to the ports.
\[p = \frac{9}{10} \text{ and } q = 1 - p = \frac{1}{10}\]
\[\text{ Mean } = np = 450 \text{ and Variance } = npq = 45\]
\[\text{ Mean } = 450\]
\[\text{ Standard deviation } = \sqrt{45} = 6 . 71\]
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