Question 299129
Suppose that you are designing 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 a 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 0.6. 
Both women’s and men’s reach from this position is normally distributed. 
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Procedure:
Draw a normal curve for the men and another for the women.
Men's curve data:
Put 3.1 in the middle and note that the std is 0.6
z(2)= (2-3.1)/0.6 = -1.833333
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P(Men's reach is less than 2) = P(z<=-1.8333) = 0.0334
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Women's curve data;
Put 2.8 in the middle and note the std = 0.5

z(2) = (2-2.8)/0.5 = -1.6
P(women's reach is less than required) = P(z<-1.6) = 0.0548
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If this design is implemented, 
(a) what percentage of women will not be able to work on this instrument panel?
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(b) What percentage of men will not be able to work on this instrument panel?
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(c) Explain your answers to a person who has never had a course in statistics. 
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Cheers,
Stan H.
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