Straddle to implied volatility

On 6 Oct 2026 the Nifty 13 Oct 22,750 straddle closed at 305.20 with a parity forward of 22,747.10 (bhavcopy). Take $r=5.25\%$, $\tau=7/365$. (a) Estimate $\sigma$ with the linear rule. (b) The exact Black-76 inversion gives 12.154%. How large is the error of (a)? (c) With $S=22{,}776.10$, compute the one-standard-deviation weekly move in points.