Statistics

posted by .

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 -

    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 -

    .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 < (2-2.8) / 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 < (2-3.1) / 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)

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. maths

    The head of an industrial machine moves in a straight line horizontally backwards and forwards from a central position. The movement can be modelled using the sine wave d = 80 sin(pie t), where d is the horizontal distance (in cm) …
  2. maths

    The head of an industrial machine moves in a straight line horizontally backwards and forwards from a central position. The movement can be modelled using the sine wave d = 80 sin ( pie t), where d is the horizontal distance (in cm) …
  3. math

    The head of an industrial machine moves in a straight line horizontally backwards and forwards from a central position. The movement can be modelled using the sine wave d = 80 sin ( pie t), where d is the horizontal distance (in cm) …
  4. math

    The head of an industrial machine moves in a straight line horizontally backwards and forwards from a central position. The movement can be modelled using the sine wave d = 80 sin ( pie t), where d is the horizontal distance (in cm) …
  5. math

    The head of an industrial machine moves in a straight line horizontally backwards and forwards from a central position. The movement can be modelled using the sine wave d = 80 sin ( pie t), where d is the horizontal distance (in cm) …
  6. maths

    The head of an industrial machine moves in a straight line horizontally backwards and forwards from a central position. The movement can be modelled using the sine wave d = 80 sin ( pie t), where d is the horizontal distance (in cm) …
  7. maths

    would it be number 6? The head of an industrial machine moves in a straight line horizontally backwards and forwards from a central position. The movement can be modelled using the sine wave d = 80 sin ( pie t), where d is the horizontal
  8. Physics

    A machine carries a 4.5 kg package from an initial position of di = (0.50 m) + (0.75 m) + (0.20 m) at t = 0 to a final position of df = (7.60 m) + (12.0 m) + (7.30 m) at t = 11 s. The constant force applied by the machine on the package …
  9. Physics

    A machine carries a 3.0 kg package from an initial position of di = (0.50 m) + (0.75 m) + (0.20 m) at t = 0 to a final position of df = (7.30 m) + (11.0 m) + (7.20 m) at t = 14 s. The constant force applied by the machine on the package …
  10. college finite math

    A product may be made using Machine I or Machine II. The manufacturer estimates that the monthly fixed costs of using Machine I are $17,000, whereas the monthly fixed costs of using Machine II are $14,000. The variable costs of manufacturing …

More Similar Questions