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4 December, 04:43

According to the U. S. Department of Agriculture, Alabama egg farmers produce millions of eggs every year. Suppose egg production per year in Alabama is normally distributed, with a standard deviation of 83 million eggs. If during only 3% of the years Alabama egg farmers produce more than 2,655 million eggs, what is the mean egg production by Alabama farmers?

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  1. 4 December, 05:03
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    The mean egg production 2499 million

    Step-by-step explanation:

    P (Z > a) = 3% = 0.03

    P (Z > a) = 1 - ∅ (a)

    1 - ∅ (a) = 0.03

    ∅ (a) = 1 - 0.03

    ∅ (a) = 0.97

    Checking the normal distribution curve, for ∅ (a) = 0.97, z = 1.88

    This means that area under the normal curve is 3% (0.03) to the right of z = 1.8808

    X = μ + (zб)

    X = 2,655 millions

    б = 83 million

    2655 = μ + (1.88 * 83)

    2655 = μ + 156.04

    μ = 2655 - 156.04

    μ = 2498.96

    The mean egg production, is therefore, 2499 million
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