A population has a mean muequals160 and a standard deviation sigmaequals20. Find the mean and standard deviation of the sampling distributio

Question

A population has a mean muequals160 and a standard deviation sigmaequals20. Find the mean and standard deviation of the sampling distribution of sample means with sample size nequals58

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Madelyn 4 weeks 2021-09-16T02:42:04+00:00 1 Answer 0

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    2021-09-16T02:43:05+00:00

    Answer:

    Mean 160

    Standard deviation 2.63

    Step-by-step explanation:

    The Central Limit Theorem estabilishes that, for a random variable X, with mean \mu and standard deviation \sigma, the sample means with size n of at least 30 can be approximated to a normal distribution with mean \mu and standard deviation s = \frac{\sigma}{\sqrt{n}}

    In this problem, we have that:

    \mu = 160, \sigma = 20

    Find the mean and standard deviation of the sampling distribution of sample means with sample size n = 58.

    Mean 160

    Standard deviation s = \frac{20}{\sqrt{58}} = 2.63

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