On December $2,2016,$ shares of MMM were valued at $S_0=$$$172\mathrm{.}43.$ Short term

interest rates at that time were approximately $r=0\mathrm{.}0034.$ Quoted prices for call

options on MMM with maturity December $9,2016(=\frac{7}{360})$ on December $2$ were:

Compute the implied volatility corresponding to the options with strike prices $165,$

$172\mathrm{.}5,$ and $180.$

Plot the implied volatilities you computed in the previous problem as a function of

the strike price. Place implied volatility on the vertical axis and strike price on the

horizontal axis. What characteristic shape does the data display?