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.

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Solution

Total number of ships (n) = 500
Let X denote the number of ships returning safely to the ports.
$p = \frac{9}{10} and q = 1 - p = \frac{1}{10}$

$Mean = n p = 450 and Variance = n p q = 45 Mean = 450 Standard deviation = \sqrt{45} = 6.71$

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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.

Total number of ships (n) = 500 Let X denote the number of ships returning safely to the ports. p=910 and q =1-p =110 Mean = np = 450 and Variance =npq = 45 Mean =450 Standard deviation = 45 = 6.71

Total number of ships (n) = 500
Let X denote the number of ships returning safely to the ports.
$p = \frac{9}{10} and q = 1 - p = \frac{1}{10}$

$Mean = n p = 450 and Variance = n p q = 45 Mean = 450 Standard deviation = \sqrt{45} = 6.71$