Cumulative probability of Gaussian distribution + Confidence Intervals + Point and Error bars

Hello everyone. I have a quite specific problem. I want to reproduce a plot that has been generated in Matlab I believe. Imagine we have the following data set:

1  100
2 105
3 90
4 120
5 108
6 92
7 111
8 109

Problem: Now I want to plot the cumulative probability of the second column as "points" with the horizontal error bars (plus and minus standard error). Plus I want to find the Gaussian distribution using Maximum Likelihood method and also fit plot its cumulative probability with 3 different confidence intervals on top of the previous plot.

What I can already do: using stat_ecdf I can draw the empirical cumulative probability. However I don't know how to add the error bars and Gaussian distribution.

I would appreciate any help or source on this. Thanks a lot!

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