the process improvement manager has developed a new machine to cut materials for running shoes. the material cannot be more than $0\mathrm{.}02$ of an inch from the required thickness of $\mathrm{.}455$ inches. when you took samples $(15$ samples with $10$ observavtions in each sample$)$ of materials cut from the new machine, you calculated the following data:

x$-$double bar$=0\mathrm{.}460,$ R$-$bar$=0\mathrm{.}15$