Giúp em với huhu, bài này khó

a) Quy tắc $2\sigma:$

$\quad P(\mu - 2\sigma < X < \mu + 2\sigma) = \phi\left(\dfrac{(\mu + 2\sigma) - \mu}{\sigma}\right) + \phi\left(\dfrac{(\mu - 2\sigma) - \mu}{\sigma}\right)$

$\Leftrightarrow P(\mu - 2\sigma < X < \mu + 2\sigma) = \phi(2) - \phi(-2)$

$\Leftrightarrow P(\mu - 2\sigma < X < \mu + 2\sigma) = 2\phi(2)$

$\Leftrightarrow P(\mu - 2\sigma < X < \mu + 2\sigma) = 2\cdot 0,4772$

$\Leftrightarrow P(\mu - 2\sigma < X < \mu + 2\sigma) = 0,9544$

$\Leftrightarrow P(\mu - 2\sigma < X < \mu + 2\sigma) = 95,44\%$

a) Quy tắc $3\sigma:$

$\quad P(\mu - 3\sigma < X < \mu + 3\sigma) = \phi\left(\dfrac{(\mu + 3\sigma) - \mu}{\sigma}\right) + \phi\left(\dfrac{(\mu - 3\sigma) - \mu}{\sigma}\right)$

$\Leftrightarrow P(\mu - 2\sigma < X < \mu + 2\sigma) = \phi(3) - \phi(-3)$

$\Leftrightarrow P(\mu - 2\sigma < X < \mu + 2\sigma) = 2\phi(3)$

$\Leftrightarrow P(\mu - 2\sigma < X < \mu + 2\sigma) = 2\cdot 0,4987$

$\Leftrightarrow P(\mu - 2\sigma < X < \mu + 2\sigma) = 0,9974$

$\Leftrightarrow P(\mu - 2\sigma < X < \mu + 2\sigma) = 99,74\%$