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28 September, 02:04

The mean weight of loads of rock is 51.0 tons with a standard deviation of 10.0 tons. If 36 loads are chosen at random for a weight check, find the probability that the mean weight of those loads is less than 50.3 tons. Assume that the variable is normally distributed.

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  1. 28 September, 02:25
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    0.3372

    Step-by-step explanation:

    Mean weight (μ) = 51.0 tons

    Standard deviation (σ) = 10.0 tons

    n = 36

    Pr (x<50.3) = ?

    Using normal distribution,

    Z = (X - μ) / σ/√n

    When X = 50.3

    Z = (50.3 - 51.0) / 10/√36

    Z = - 0.7 / 10/6

    Z = - 0.42

    From the normal distribution table, 0.42 = 0.1628

    Φ (z) = 0.1628

    Recall that when Z is negative, Pr (x
    Pr (x < 50.3) = 0.5 - 0.1628

    = 0.3372
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