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27 March, 01:48

In a certain city, the average 20 - to 29-year old man is 72.5 inches tall, with a standard deviation of 3.2 inches, while the average 20 - to 29-year old woman is 64.5 inches tall, with a standard deviation of 3.8 inches. Who is relatively taller, a 75-inch man or a 70-inch woman?

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  1. 27 March, 04:18
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    70-inch woman is taller.

    Step-by-step explanation:

    Given dа ta:

    For men

    age group = 20 - 29 year

    Height = 72.5 inches

    standard deviation = 3.2 inches

    For women

    age group = 20 - 29 year

    Height = 64.5 inches

    standard deviation = 3.8 inches

    To find:

    who is taller? a 75-inch man or a 70-inch woman?

    To find that, firstly we find z - score for each gender.

    Solve:

    Z-score = (x-μ) / σ

    where:

    μ=mean

    σ=std deviation

    Z (men) = (75-72.5) / 3.2

    = 0.781

    Z (women) = (70-64.5) / 3.8

    = 1.447

    From the above, the z-score for the woman is relatively larger than that of the man, this means that the woman is taller.
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