Stock X price is $$100$ and could go up by $17\%$ or down by $15\%$ in each six$-$month period. A one$-$year put option on stock X has an exercise price of $$98.$ The interest rate is $2\mathrm{.}5\%$ a year.

$($a$)$ Find a equivalent standard deviation of returns of stock X$.$

$($b$)$ What is the value of the put?