If on an average 9 ships out of 10 arrive safely to ports, find the mean and S.D. of ships returning safely out of a total of 500 ships.

Explanation

Total number of ships` (n)=500`

Let `X` denote the number of ships returning safely to the ports.
` p=frac{9}{10} and q=1-p=frac{1}{10}`

Mean `=n p=450` and Variance `=n p q=45`

Mean` =450`

Standard deviation `=sqrt{45}=6.71`