Statistics
posted by Lamont Sanford on .
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?

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 
.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)