$1)$Set the height of a keyboard so that the seated operator can have his or her forearms and wrists horizontal. Elbow height in a sitting position for women has a mean of $220\mathrm{.}5$mm with a standard deviation of $26\mathrm{.}8$mm and for men $=230\mathrm{.}6$mm $\backslash$sigma $=27\mathrm{.}2$mm$.$ What adjustable range should the keyboard have? Assume that adjusting from the $10$th percentile for women to the $90$th percentile for men would be appropriate.

$2)$Determine the torque necessary to close the critical lever that shuts down a chemical plant, so that the weakest operator can use it in the event of an emergency. Also consider that the lever must be structurally sound so that the brute force of a strong operator will not break it$.$ break At the plant, the push and pull force of a sample of $100$ employees was measured. It was determined that the pushing force of the weak hand has $=116$ N and $\backslash$sigma $=37$N$,$ while the pulling force of combined hands has $=331$ N and $\backslash$sigma $=173$N$.$ Explain which percentile you should consider to design the structural strength of the lever and calculate the respective strength. Explain what percentile you should consider for the lever operating force and calculate the respective force.