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12 November, 04:28

For certain workers, the mean wage is $5.00/hr, with a standard deviation of $0.25. If a worker is chosen at random, what is the probability that the workers wage is between $4.25-$5.75. Assume a normal distribution of wages.

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Answers (2)
  1. 12 November, 04:29
    0
    P (-3.0 < z < 3.0) = 0.9974

    Step-by-step explanation:

    Mean = 5

    Standard Deviation = 0.25

    We need to find P (4.25
    z = x - mean/standard deviation

    z = 4.25 - 5/0.25

    z = - 3.0

    z = x - mean/standard deviation

    z = 5.75 - 5/0.25

    z = 3.0

    So, P (4.25
    Finding values from the z-score table

    P (z<-3.0) = 0.0013

    P (z<3.0) = 0.9987

    P (-3.0 < z < 3.0) = P (z<3.0) - P (z<-3.0)

    P (-3.0 < z < 3.0) = 0.9987 - 0.0013

    P (-3.0 < z < 3.0) = 0.9974
  2. 12 November, 04:37
    0
    The probability is 0.9973 or 99.73%

    Step-by-step explanation:

    * Lets explain how to solve the problem

    - For the probability that a < X < b (X is between two numbers, a and b),

    convert a and b into z-scores and use the table to find the area

    between the two z-values.

    - Lets revise how to find the z-score

    - The rule the z-score is z = (x - μ) / σ, where

    # x is the score

    # μ is the mean

    # σ is the standard deviation

    * Lets solve the problem

    - For certain workers, the mean wage is $5.00/hr, with a standard

    deviation of $0.25

    ∴ μ = 5 and σ = 0.25

    - The worker wage is between $4.25 and $5.75

    ∴ 4.25 < X < 5.75

    ∵ z = (x - μ) / σ

    ∴ z = (4.25 - 5) / 0.25 = - 0.75/0.25 = - 3

    ∴ z = (5.75 - 5) / 0.25 = 0.75/0.25 = 3

    - Use the z table to find the corresponding area

    ∵ P (z > - 3) = 0.00135

    ∵ P (z < 3) = 0.99865

    ∴ P (-3 < z < - 2) = 0.99865 - 0.00135 = 0.9973

    ∵ P (4.25 < X < 5.75) = P (-3 < z < 3)

    ∴ P (4.25 < X < 5.75) = 0.9973 = 99.7%

    * The probability is 0.9973 or 99.73%
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