Petey creates a portfolio by investing $75\%$ of his savings in shares of Antsy and the rest in shares of Bugsy.

The expected return on Antsy's stock is $8\%,$ the standard deviation of the stock's returns is $0\mathrm{.}200.$

The expected return on Bugsy's stock is $10\%,$ the standard deviation of the stock's returns is $0\mathrm{.}500.$

What is the minimum possible standard deviation of the portfolio?

$[$Note: you have all the information you need.$]$