Control Theory problem estimating damping and frequency from step response data

I have a homework question to generate the Laplace transfer function from unit step response data which the lecturer has generated with Simulink. The tf should be 10.108/(s^2+2.128s+14.44). I have measured parameters from a plot of data giving: overshoot(os)% = 28.2%, settling time = 6.5s and peak time = 0.9s. Steady state value = 0.7. From this I have calculated damping factor using z = -ln(0.282)/(sqrt(pi^2+ln^2(0.282)) = 0.374. I then use this to calculate natural frequency wn = 4/(z x 6.5) = 1.645. But these numbers are not the correct values which should be z = 0.28 and wn = 3.8.

The lecturer has checked my calculations are correct and also that my plot measurements agree with the Simulink LTI plot. So, I have no idea what I am doing wrong. Is there a reason why the equations for z and wn would not work with this transfer function or plot?

[Babak]

Are you given the Simulink model or the transfer function or the step response plot? I mean what data you used to compute the overshoot, settling time,...?