In a particular population of polar bears, the adult males have masses that are normally distributed with mean $515$ kilograms and standard deviation of $88$ kilograms.

$($a$)$ An adult male is chosen t random from this population. Calculate the probability that his mass is Between $480$ and $580$ kilograms

$($ii$)$Less than $600$ kilograms

$($iii$)$More than $450$ kilograms

$($b$)$ What is the minimum mass required for a bear to be amongst the heaviest $20\%$ of adult males in this population?