the austrainian sheep dog is a breed renowned for its intelligence and work ethic.it is estimated that 45% of adult Australian sheep dogs we

Question

the austrainian sheep dog is a breed renowned for its intelligence and work ethic.it is estimated that 45% of adult Australian sheep dogs weigh 65 pounds or more. a sample of 15 adult dogs is studied.what is the standard deviation of the number of dogs who weigh 65 ils or more

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Natalia 2 weeks 2022-01-03T05:23:22+00:00 1 Answer 0 views 0

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    2022-01-03T05:24:25+00:00

    Answer:

    The standard deviation of the number of dogs who weigh 65 pounds or more is 1.93.

    Step-by-step explanation:

    For each dogs, there are only two possible outcomes. Either they weigh less than 65 pounds, or they weight at least 65 pounds. The probability of a dog weighing more than 65 pounds is independent of other dogs. So we use the binomial probability distribution to solve this question.

    Binomial probability distribution

    Probability of exactly x sucesses on n repeated trials, with p probability.

    The standard deviation of the binomial distribution is:

    \sqrt{V(X)} = \sqrt{np(1-p)}

    It is estimated that 45% of adult Australian sheep dogs weigh 65 pounds or more.

    This means that p = 0.45

    Sample of 15 adult dogs is studied.

    This means that n = 15

    What is the standard deviation of the number of dogs who weigh 65 pounds or more

    \sqrt{V(X)} = \sqrt{np(1-p)}[ = \sqrt{15*0.45*0.55} = 1.93

    The standard deviation of the number of dogs who weigh 65 pounds or more is 1.93.

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