$(10$ points$)$ Recall the anthropometry homework. The spot$-$welding job is shown in the picture below. The redesign criterion is that the operators do not raise their hand above shoulder $($cause of shoulder stress and pain$).$ As an ergonomist, you plan to design a height adjustable platform to accommodate more than $90\%$ of both male and female workers. Based on the anthropometric data in the right table, please estimate the required range of the platform height $($minimum to maximum height$).$ Please take into account the effects of shoe height and clearly list your assumptions.