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31 October, 12:45

According to the website nationalbikeregistry, at the campus of UC Berkeley 12% of registered bicycles are stolen each year. Suppose a random sample of 160 registered bicycles at UC Berkeley is selected. Let the random variable X be the number of bicycles that were stolen in the past year. What are the values of the parameters for the binomial random variable X?

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  1. 31 October, 16:17
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    n = 160

    p = 0.12

    Explanation:

    In a Binomial distribution two parameters are of great interest, n and p.

    where n is the number of trials and p is the probability of success and (1 - p) is the probability of failure.

    p = 12%

    n = 160

    Mean = E (X) = μ = n*p = 160*0.12 = 19.2

    μ = 19.2

    variance = σ² = np (1 - p) = 160*0.12 (1 - 0.12) = 16.89

    standard deviation = σ = √16.89 = 4.11

    σ = 4.11
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