Designing an instrument panel for a large industrial machine

Suppose that you are designing in an instrument panel for a large industrial machine.The machine requires the person using it to reach 2 feet from a particular position. The reach from this position for adult women is known to have mean of 2.8 feet with a standard deviation of .5. The reach for adult men is known to have a mean of 3.1 feet with a standard deviation of .6 . Both women’s and men’s reach from this position is normally distributed. If this design is implemented, (a) what percentage of women will not be able to work on this instrument panel? (b) What percentage of men will not be able to work on this instrument panel? (c) Explain your answers to a person who has never had a course in statistics.

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