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the average woman's height is 65 inches with a standard deviation of 3.5 inches. what proportion of women are shorter than 62inches tall

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  1. 23 May, 20:28
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    19.77%

    Step-by-step explanation:

    Given

    Mean = μ=65 inches

    SD = σ=3.5 inches

    We have to find the proportion of women whose height is less than 62 inches.

    For that we have to calculate z-score for the given value first. The z-score of a value tells us that how many standard deviations the value is far from mean. The area to the left of the z-score gives the proportion of data that is less than the z-score value and the area to the right gives the proportion.

    So,

    z-score of 62 = (x-μ) / σ

    = (62-65) / 3.5

    = (-3) / 3.5

    z-score of 62 = - 0.8571

    To find the area to the left of the z-score, the z-score table is used which is easily available on the internet.

    The area to the left of the z-score is 1.97662.

    To find the proportion/percentage of women whose height is less than 62, the area has to be multiplied by 100.

    Percentage of women whose height is less than 62 inches=0.197662*100

    =19.77%
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