Posted by Lamont Sanford on Tuesday, August 5, 2014 at 1:59am.
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:
What percentage of women will not be able to work on this instrument panel?
What percentage of men will not be able to work on this instrument panel?

Statistics  Steve, Tuesday, August 5, 2014 at 5:01am
for women, 2 ft is 1.6 std below the mean
for men, 2 ft is 3.33 std below the mean.
So, look those up in your Z table to see the break points.
Or, play around at
http://davidmlane.com/hyperstat/z_table.html

Statistics  Anonymous, Sunday, March 8, 2015 at 4:12pm
.For women:
Mean = 2.8
SD = 0.5
P( x < 2) =
μ = 2.8
σ = 0.5
standardize x to z = (x  μ) / σ
P(x < 2) = P( z < (22.8) / 0.5)
= P(z < 1.6) = 0.0548  5.48 percent of women won't be able to work on this instrument panel
(From Normal probability table)
Men:
Mean = 3.1
SD = 0.6
P( x < 2) =
μ = 3.1
σ = 0.6
standardize x to z = (x  μ) / σ
P(x < 2) = P( z < (23.1) / 0.6)
= P(z < 1.8333) = 0.0336  3.36 percent of men won't be able to work on this instrument panel
(From Normal probability table)
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