'How can I draw a line in a python plot indicating 1 standard deviation?

I have a plot from a data frame, I want to to draw a line indicating one standard deviation from the mean like in the picture below.

enter image description here

I know how to add text in the plot, but what I don´t know is how to add the line that represents the exact size of 1 standard deviation. In my plot, I fitted a 3 order polynomial and I draw two lines indicating 3 standard deviations from the fitted curve, but I haven´t come up with an idea in order to do what I intend. I would really appreciate your help. Next I put the current picture of my plot and my code
enter image description here

popt, pcov = curve_fit(func,date2num(x),y)
plt.plot(date2num(x), func(date2num(x),*popt), linestyle='--', linewidth=2, color='darkslategrey')
plt.plot(date2num(x), func(date2num(x),*popt)+(3*(np.sqrt(np.mean(func(date2num(GLE_48['Date and Time']),*popt))))), linestyle='--', linewidth=1.5, 
color='black')
plt.plot(date2num(x), func(date2num(x),*popt)-(3*(np.sqrt(np.mean(func(date2num(GLE_48['Date and Time']),*popt))))), linestyle='--', linewidth=1.5, color='black'


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