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17 December, 04:48

Consider a normal distribution curve where the middle 65 % of the area under the curve lies above the interval (3, 17). Use this information to find the mean, μ, and the standard deviation, σ, of the distribution. a) μ = b) σ=

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  1. 17 December, 07:10
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    Mean = μ = 10

    Standard deviation = σ = 18.42

    Step-by-step explanation:

    We know that in normal distribution,

    μ ± z*σ

    Where μ is the mean, σ is the standard deviation and z is the corresponding z-score

    Upper value = μ + z*σ

    Lower value = μ - z*σ

    The z-score corresponding to 65 percentile is 0.38

    17 = μ + 0.38*σ eq. 1

    3 = μ - 0.38*σ eq. 2

    Add eq. 1 and eq. 2

    20 = 2μ

    μ = 20/2

    μ = 10

    substitute μ = 10 into eq. 1

    17 = 10 + 0.38*σ

    0.38*σ = 17 - 10

    σ = 7/0.38

    σ = 18.42

    Therefore, the mean is 10 and standard deviation is 18.42
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