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.

Answer 1

Total number of ships (n)  = 500

Let X denote the number of ships returning safely to the ports.

\[p = \frac{9}{10} \text{ and } q = 1 - p = \frac{1}{10}\]

\[\text{ Mean } = np = 450 \text{ and Variance }  = npq = 45\]

\[\text{  Mean } = 450\]

\[\text{  Standard deviation } = \sqrt{45} = 6 . 71\]