When you post a picture on social media, it seems like your friends randomly "like" the picture. Independent of the quality or the humor of the photo, there seems to be a 21.8% chance of the picture being "liked" for any given picture.

Let X represent the number of pictures you post until one is "liked." (X represents the photo number that is actually liked.) Find:
$\displaystyle \mu_{{X}}$:

$\displaystyle \sigma_{{X}}$:

$\displaystyle {P}{\left({X}={6}\right)}$:

$\displaystyle {P}{\left({X}<{11}\right)}$:

$\displaystyle {P}{\left({X}>{12}\right)}$:

$\displaystyle {P}{\left({8}\le{X}\le{10}\right)}$: