On the distant planet Cowabunga, the weights of cows have a normal distribution with a mean of 483 pounds and a standard deviation of 70 pou

Question

On the distant planet Cowabunga, the weights of cows have a normal distribution with a mean of 483 pounds and a standard deviation of 70 pounds. The cow transport truck holds 5 cows and can hold a maximum weight of 2840. If 5 cows are randomly selected from the very large herd to go on the truck, what is the probability their total weight will be over the maximum allowed of 2840

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Neala 3 years 2021-09-04T10:19:11+00:00 1 Answers 16 views 0

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  1. kimcuc
    0
    2021-09-04T10:20:11+00:00
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    Answer: 0.0033

    Step-by-step explanation:

    Let x be a random variable that denotes the weights of cows.

    Given: \mu = 483,\ \sigma=70

    maximum weight can be hold= 2840 pounds.

    Mean weight = \frac{2840}{5} = 568 pounds

    The probability their total weight will be over the maximum allowed of 2840

    = P(X>2840)

    P(\dfrac{x-\mu}{\dfrac{\sigma}{\sqrt{n}}}>\dfrac{568-483}{\dfrac{70}{\sqrt{5}}})\\\\=P(z>2.715)\\\\=1-P(z<2.715)\\\\=1-0.9967=0.0033

    Hence, the required probability = 0.0033

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