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24 May, 23:33

The upper leg length of 20 to 29-year-old males is normally distributed with a mean length of 43.7 cm and a standard deviation of 4.2 cm. a random sample of 9 males who are 20 to 29 years old is obtained. what it the probability that the mean leg length is less than 20 cm? 0.1894 pratically 0 0.2134 0.7898

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  1. 25 May, 02:48
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    Given:

    μ = 43.7 cm, the population mean

    σ = 4.2 cm, the population standard deviation.

    We want to test against the population statistics with

    n = 9, the sample size,

    x = 20 cm, the random variable.

    We want to find P (x < 20).

    Calculate the z-score.

    z = (x - μ) / σ

    = (20 - 43.7) / 4.2

    = - 5.643

    From the standard tables, obtain

    P (z < - 5.643) = 0 (actually about 8.5 x 10⁻⁹)

    Answer: Practically zero.
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