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15 August, 19:49

If 75% of men spend more than $75 monthly on clothes, while 15% pay more than $150, what is the mean monthly expense on clothes and what is the standard deviation?

/mu=84.33, / sigma=13.44

/mu=104.39, / sigma=43.86

/mu=118.42, / sigma=56.16

/mu=139.43, / sigma=83.36

/mu=54.43, / sigma=13.22

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Answers (1)
  1. 15 August, 19:54
    0
    We are given that 75% of men spend more than $75 on clothes, while

    15% of men spend more than $150.

    To solve this problem, we assume the

    mean = m, and

    standard deviation = s.

    Then

    P (X>75) = 1-P (X<75) = 0.75=1-P ((75-m) / s<75) = 0.75

    (75-m) / s=Z (P=1-0.75) = - 0.6744898 [ last value from tables ]

    giving equation

    75-m=-0.6744898s ... (1)

    Similarly

    P (X>150) = 1-P (X<150) = 0.15=1-P ((150-m) / s<150) = 0.15

    (150-m) / s=Z (P = (1-0.15) = 1.036433

    or

    150-m=1.036433s ... (2)

    Solving the system of equations (1) and (2) for m and s gives

    m=104.57

    s=43.84

    which is exactly what we need.

    Substitute mu=m, and sigma=s allows you to find the answer choice.
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