a) In a simple random sample of 1000 faculty taken among all universities in a country, the number of papers published by the individual sam

Question

a) In a simple random sample of 1000 faculty taken among all universities in a country, the number of papers published by the individual sampled faculty in the past year had a mean of 1.1 and an SD of 1.8. Does the Central Limit Theorem say that the distribution of the number of papers published by the individual sampled faculty in the past year is roughly normal

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Kim Cúc 6 months 2021-07-23T11:38:58+00:00 1 Answers 22 views 0

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    2021-07-23T11:40:20+00:00

    Answer:

    According to the Central Limit theorem, the distribution is roughly normal

    Step-by-step explanation:

    The Central Limit Theorem states that for sample sizes above 30 and not withstanding population distribution’s shape, the sampling distribution of the sample mean becomes more similar t hat of a normal distribution as the sample size increases;

    The size of the sample = 1,000 >> 30

    As the sample size approaches infinity, we have;

    z=\dfrac{\bar{x}-\mu }{\dfrac{S.D.}{\sqrt{n}}}

    \overline x = 1.5

    S.D. = 1.8

    n = 1000

    Assume μ = 1, we get;

    P(x > 1.1):z=\dfrac{1.1-1 }{\dfrac{1.8}{\sqrt{1000}}} = 1.7568

    P(z > 1.7568) = 1 – 0.96080 = 0.0392

    Therefore, it is very likely that the mean of the population is not larger than the sample mean

    Therefore, yes, the Central Limit Theorem say that the distribution of the number of papers published by the individual sampled faculty in the past year is roughly normal

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