$4)$ Bank XYZ uses EWMA approach to estimate the volatility using more than $4$ years of data $($more than $1\mathrm{.}000$ observations for each variable$).$ They use a lambda of $0\mathrm{.}93.$ An error has been discovered in the data entry of four days ago. The return introduced was $-1\mathrm{.}5\%,$ when in reality the return had been $15\%.$ The volatility estimate before finding the error was $4\mathrm{.}00\%.$ After correcting the value, in which

interval will be the new estimate of volatility?

a$)$ Between $4\mathrm{.}01\%$ and $4\mathrm{.}50\%$

b$)$ Between $4\mathrm{.}51\%$ and $5\mathrm{.}00\%$

c$)$ Between $5\mathrm{.}01\%$ and $5\mathrm{.}50\%$

d$)$ Between $5\mathrm{.}51\%$ and $6\mathrm{.}00\%$

The correct asnwer is c$),$ please explain each step