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14 October, 01:36

Use the given values of n and p to find the minimum usual value μ - 2σ and the maximum usual value μ + 2σ. Round your answer to the nearest hundredth unless otherwise noted. n = 1042, p = 0.80

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  1. 14 October, 01:58
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    Given Information:

    number of trials = n = 1042

    Probability of success = p = 0.80

    Required Information:

    Maximum usual value = μ + 2σ = ?

    Minimum usual value = μ - 2σ = ?

    Answer:

    Maximum usual value = 859.51

    Minimum usual value = 807.78

    Step-by-step explanation:

    In a binomial distribution, the mean μ is given by

    μ = np

    μ = 1042*0.80

    μ = 833.6

    The standard deviation is given by

    σ = √np (1 - p)

    σ = √1042*0.80 (1 - 0.80)

    σ = √833.6 (0.20)

    σ = 12.91

    The Maximum and Minimum usual values are

    μ + 2σ = 833.6 + 2*12.91

    μ + 2σ = 833.6 + 25.82

    μ + 2σ = 859.51

    μ - 2σ = 833.6 - 25.82

    μ - 2σ = 807.78

    Therefore, the minimum usual value is 807.78 and maximum usual value is 859.51
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