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21 April, 01:23

It is estimated that 25% of households own a riding lawn mower. A sample of 16 households is studied. What is the probability that exactly 5 of these own a riding lawn mower?

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  1. 21 April, 05:23
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    From the data provided:

    p = 25% = 0.25

    1-p = 1-0.25 = 0.75

    Sample size, n = 16

    (n-k) = 16-5 = 11

    k = 5

    Probability that exactly 5 selected from the sample have lawn mower:

    p (k=5) = (n, k) * p^k * (1-p) ^ (n-k) = [n! / (k) ! (n-k) !]*p^k * (1-p) ^ (n-k) = [16! / (5) ! (16-5) !]*0.25^5 * (1-0.25) ^ (16-5) = 4368 * (1/1024) * 0.04224 = 0.1802

    Therefore, probability that selected 5 households have a lawn mower is 0.1802 = 18.02%.
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