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6 May, 23:21

Major league baseball salaries averaged $3.26 million with a standard deviation of $1.2 million in a recent year. suppose a sample of 100 major league players was taken. find the approximate probability that the mean salary of the 100 players exceeded $4.0 million.

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  1. 6 May, 23:33
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    Given:

    μ = $3.26 million, averaged salary

    σ = $1.2 million, standard deviation

    n = 100, sample size.

    Let x = random test value

    We want to determine P (x>4).

    Calculate z-score.

    z = (x - μ) / (σ/√n) = (4 - 3.26) / (1.2/10) = 6.1667

    From standard tables,

    P (z<6.1667) = 1

    The area under the distribution curve = 1.

    Therefore

    P (z>6.1667) = 1 - P (z<=6.1667) = 1 - 1 = 0

    Answer: The probability is 0.
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