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Assume that women's heights are normally distributed with a mean=63.6 in. and standard deviation = 2.5 in.

a) To be eligible for the US Marine Corps, a woman must have a height between 58 in. and 73 in. Find the percentage of women who satisfy that requirement.

b)If the requirement is changed to exclude the shortest 1% and exclude the tallest 1%, find the heights that are acceptable.

  • statistics -

    Use z-scores for both a) and b).

    Formula:

    z = (x - mean)/sd

    a) Find both z-scores.
    First z: x = 58, mean = 63.6, sd = 2.5
    Second z: x = 73, mean = 63.6, sd = 2.5

    Once you have both z-scores, check a z-table for the probability between the two scores. Convert to a percentage.

    b) Find the two z-scores using a z-table for the shortest 1% and the tallest 1%. Once you have both z-scores, find x for both using the formula above, then go from there.

    I hope this will help get you started.

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