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hamrogers
Lv 6
hamrogers asked in Science & MathematicsMathematics · 10 years ago

stats question: find percentage?

I can't find an example in my textbook. If you could show me the equation I'd appreciate it. The question goes like this.

Men's heights are normally distributed with the mean 69.0 inches, standard deviation 2.8 inches.

The US Marines require men to be between 64 and 80 inches tall. Find the percentage of men who meet this requirement.

Thanks for your assistance.

2 Answers

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  • ?
    Lv 4
    10 years ago
    Favorite Answer

    You need to use standard z-score for this. The z value is (value - mean)/sigma

    z = (80-69)/2.8 = 3.9

    z = (64-69)/2.8 = -1.8

    Then go on your graphing calculator and press 2nd Vars, normalcdf(

    normalcdf(-1.8, 3.9) = .9640 = 96.4%

  • Guillermo
    Lv 7
    10 years ago

    Let X be men's heights.

    X ∼ n(69; 2.8)

    P(64 ≤ X ≤ 80) = P((64 - 69)/2.8 ≤ (X - 69)/2.8 ≤ (80 - 69)/2.8) = P( - 1.79 ≤ Z ≤ 3.93) =

    P(Z ≤ 3.93) - P(Z ≤ - 1.79) = 1 - 0.0367 = 0.9633*100 = 96.33%

    Source(s): Standardized Normal Distribution.
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