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 .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.
Sooo stuck!!!! Please help!!!
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! 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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