A population of cats has a population mean of μ = 12μ=12pounds and a population standard deviation of σ = 2.0σ=2.0pounds. The distribution o

Question

A population of cats has a population mean of μ = 12μ=12pounds and a population standard deviation of σ = 2.0σ=2.0pounds. The distribution of weights of these cats is fairly symmetrical. If you take a random sample of 100 cats from this population, what will be the resulting sampling distribution of x?

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Hadley 1 week 2021-10-12T07:16:46+00:00 1 Answer 0

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    2021-10-12T07:18:43+00:00

    Answer:

    Normal (12, 0.20)

    Step-by-step explanation:

    Given that a population of cats has a population mean of

    \mu = 12pounds\\\sigma = 2 pounds

    Also given that the distribution of weights of these cats is fairly symmetrical.

    Since sample size is large and a random sample of 100 cats are drawn from this population, we find that

    the mean of the sample would follow a normal distribution with mean =population mean and std deviation = population std dev/sqrt n

    i.e. Sampling distribution of X would be normal with

    mean = 12 pounds

    and std deviation = \frac{2}{\sqrt{100} } \\=0.20

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