The heights of adult men in America are normally distributed, with a mean of 69.8 inches and ...?

The heights of adult men in America are normally distributed, with a mean of 69.8 inches and a standard deviation of 2.67 inches. The heights of adult women in America are also normally distributed, but with a mean of 64.8 inches and a standard deviation of 2.55 inches.

a) If a man is 6 feet 3 inches tall, what is his z-score (to two decimal places)?

Z=

b) What percentage of men are SHORTER than 6 feet 3 inches? Round to nearest tenth of a percent.

c) If a woman is 5 feet 11 inches tall, what is her z-score (to two decimal places)?

Z=

d) What percentage of women are TALLER than 5 feet 11 inches? Round to nearest tenth of a percent.

1 Answer

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  • Mike G
    Lv 7
    6 months ago
    Favorite Answer

    a) μ = 69.8

    σ = 2.67

    z(x=75) = (75-69.8)/2.67) = 1.9475

    Answer 1.95

    b) P(z<1.9475 = 0.9744

    Answer 97.4%

    c) μ = 64.8

    σ = 2.55

    z(x=71) = 2.4314

    Answer 2.43

    d) P(z>2.4314) = 0.0075

    Answer 0.8%

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