IMathAS-libretexts

Here again is the probability distribution of Y—the number of defective parts in an hour in Yves' production line:

$\displaystyle {y}$	0	1	2	3	4
$\displaystyle {P}{\left({Y}={y}\right)}$	.05	.05	.10	.75	.05

Which of the following expressions represents the standard deviation of Y?

$\displaystyle \sqrt{{{\left({.05}-{2}\right)}^{{2}}\cdot{0}+{\left({.05}-{2}\right)}^{{2}}\cdot{1}+{\left({.1}-{2}\right)}^{{2}}\cdot{2}+{\left({.75}-{2}\right)}^{{2}}\cdot{3}+{\left({.05}-{2}\right)}^{{2}}\cdot{4}}}$
$\displaystyle \sqrt{{{\left({0}-{2.7}\right)}^{{2}}\cdot{.05}+{\left({1}-{2.7}\right)}^{{2}}\cdot{.05}+{\left({2}-{2.7}\right)}^{{2}}\cdot{.10}+{\left({3}-{2.7}\right)}^{{2}}\cdot{.75}+{\left({4}-{2.7}\right)}^{{2}}\cdot{.05}}}$
$\displaystyle \sqrt{{\frac{{{\left({\left({0}-{2.7}\right)}^{{2}}\cdot{.05}+{\left({1}-{2.7}\right)}^{{2}}\cdot{.05}+{\left({2}-{2.7}\right)}^{{2}}\cdot{.10}+{\left({3}-{2.7}\right)}^{{2}}\cdot{.75}+{\left({4}-{2.7}\right)}^{{2}}\cdot{.05}\right)}}}{{{5}-{1}}}}}$
$\displaystyle \sqrt{{{\left({0}-{2.7}\right)}\cdot{.05}+{\left({1}-{2.7}\right)}\cdot{.05}+{\left({2}-{2.7}\right)}\cdot{.10}+{\left({3}-{2.7}\right)}\cdot{.75}+{\left({4}-{2.7}\right)}\cdot{.05}}}$